title: Goodluck Jonathan

text: Jonathan was named as Acting President of Nigeria on 9 February 2010, following a controversial doctrine of necessity from the Senate of Nigeria due to President Yar'Adua's trip to Saudi Arabia in November 2009 for medical treatment. On 10 February 2010, his first day as acting president, Jonathan announced a minor cabinet reshuffle.


title: Goodluck Jonathan

text: In accordance with the order of succession in the Nigerian constitution following President Yar'Adua's death on 5 May 2010, Jonathan, as Acting President, was sworn in as the substantive president of the Federal Republic of Nigeria on 6 May 2010. On 18 May 2010, the National Assembly approved Jonathan's nomination of Kaduna State Governor Namadi Sambo, to replace him as Vice President. For the general election in 2011, Jonathan and Vice President Sambo attended political events and travelled the country to campaign for the nation's highest office.


title: Goodluck Jonathan

text: A year later, on 29 May 2011 he was sworn in as President of Nigeria and Commander-in-Chief of the Armed Forces of Nigeria, becoming Nigeria's 14th Head of State. He gave his inauguration address where he declared his government was to focus on a Transformation Agenda and promised to continue implementing the seven-point agenda policy framework of President Yar'Adua. He cited anti-corruption, power and electoral reforms as focuses of his administration. He stated that he came to office under "very sad and unusual circumstances".


title: Goodluck Jonathan

text: Under Jonathan's administration, Nigeria rebased its gross domestic product for the first time in over a decade, becoming the largest economy in Africa by overtaking South Africa and Egypt.


title: Goodluck Jonathan

text: The Jonathan administration accrued over US$454 billion while in office from oil revenue. Jonathan previously served as an assistant director at the Oil Mineral Producing Areas Development commission between 1993 and 1998.


title: Goodluck Jonathan

text: The Jonathan administration oversaw the construction of new railways in the country, including the Abuja-Kaduna railway, Lagos-Ibadan railway and conceptualised high speed rail projects. Construction and beautification of many federal roads in the country, including the Lagos-Benin expressway, Abuja-Lokoja expressway, Enugu-Abakiliki expressway, Onitsha-Owerri highway and most parts of the Enugu-Port Harcourt expressway. Also, construction of the second Niger Bridge between Onitsha and Asaba to relieve the pressure on the old Niger Bridge which was completed in December 1965. Construction of airports across the country. The Akanu Ibiam Airport in Enugu was upgraded into an international airport, directly connecting the South-East region of the country to the outside world for the first time since independence.


title: Goodluck Jonathan

text: On 2 August 2010, Jonathan launched his 'Roadmap for Power Sector Reform‘. Its primary goal was to achieve stable electricity supply in Nigeria. The Power Holding Company of Nigeria, which acted as the nation's electricity provider, was broken up into 15 firms, with Nigeria handing over control of state electricity assets to 15 private bidding companies. The Nigerian government contracted for the services of CPCS Transcom Limited, a Canada-based consulting firm specialising in transportation and energy infrastructure projects, to act as the transaction adviser for the handover of state electricity assets.


title: Goodluck Jonathan

text: Historically, the Nigerian power sector has been plagued by blackouts. Economists estimate that power outages have cost Nigeria, Africa's biggest economy, billions of dollars in imported diesel for generators and lost output. In a study conducted by the World Bank, a lack of access to financing and electricity were cited as Nigeria's main obstacles to development, surpassing corruption.


title: Goodluck Jonathan

text: Jonathan suspended Sanusi Lamido Sanusi as governor of the Central Bank of Nigeria after a series of public investigations and raising the alarm on the US$20 billion NNPC scandal in a leaked letter which revealed that the Nigeria National Petroleum Corporation failed to account for US$48.9 billion of government oil revenue to the central bank – the NNPC has a history of financial irregularities and oversees the corrupt petroleum industry in Nigeria. Sanusi would go on to reveal the extent of financial recklessness that Nigeria lost a billion dollars a month to diversion of public funds under the Jonathan administration, with oil minister Diezani Alison-Madueke diverting $6 billion (₦1.2 trillion) from the Nigerian treasury.


title: Goodluck Jonathan

text: In addition, Jonathan was alleged to have personally ordered over ₦3 trillion ($15 billion) from the Central Bank of Nigeria to support his election and other self-seeking projects under the guise of an intervention fund for national security. Charles Soludo, a professor of economics and former governor of the Central Bank of Nigeria, equated Jonathan's financial recklessness to that of former Ugandan president Idi Amin. Ngozi Okonjo-Iweala, an economist and former Finance Minister of Nigeria, pegged Jonathan's administration as the main cause of Nigeria's economic woes in a lecture at George Washington University, although she later denied it. However, none of the corruption allegations against Jonathan have been proven in any law court.


title: Goodluck Jonathan

text: Jonathan's government has largely been described as corrupt. According to "The Economist", corruption flourished under the Jonathan administration, "who let politicians and their cronies fill their pockets with impunity." Large sums of money have been used improperly multiple times, with ₦3.98 trillion (US$20 billion) allegedly going missing and ₦398 billion ($2 billion) of military funds allegedly dispersed amongst high-ranking officials. In 2006, reports released by Wikileaks claimed that Jonathan's wife, Patience Jonathan, was indicted for money-laundering by Nigeria's anti-crime agency, the Economic and Financial Crimes Commission (EFCC).


title: Goodluck Jonathan

text: Since May 2015, the Muhammadu Buhari administration reportedly has been fighting corruption that was perpetrated under Jonathan. Some of the former political office holders and appointees that served under Jonathan, as well as party members, have been arrested on various corruption charges. It is alleged that some, including former Finance Minister Nenadi Usman, have returned part of the money they stole. None of these politicians have however been convicted of the alleged crimes. It remains unclear whether or not Jonathan, who is believed to have either masterminded or condoned the corruption, will be arrested.


title: Goodluck Jonathan

text: During Jonathan's administration, Nigeria's foreign policy was reviewed to reflect a "citizen-focused" approach, designed to "accord this vision of defending the dignity of humanity the highest priority" and connect foreign policy to domestic policy, while placing a greater emphasis on economic diplomacy.


title: Goodluck Jonathan

text: In January 2013, Jonathan reportedly promised $4 million to assist in cleaning up villages that have been affected by a lead poisoning incident. Over 400 children died and Human Rights Watch said that releasing the funds "could be lifesaving for countless children."


title: Goodluck Jonathan

text: On 1 January 2012, the Jonathan administration announced the start of a controversial plan to end fuel subsidies. Following the Nigeria Labour Congress' warning that the country faces many strikes, the country unions followed up with strikes that were matched with civil protests from 9–13 January 2012. Protesters and groups called for Jonathan to resign over the removal of fuel subsidies. After five days of national protests and strikes, on 16 January, Jonathan announced that the pump price of petroleum would be 97 naira per litre compared to a post-subsidy level of 147 naira.


title: Goodluck Jonathan

text: In 2012, upon the partial removal of petrol subsidies, the Jonathan administration instituted a subsidy re-investment programme designed to spend the money saved from partial petrol price deregulation on physical infrastructure such as roads, bridges, etc., across the country. The Subsidy Reinvestment and Empowerment Program (SURE-P) was also intended to improve maternal health and reduce maternal mortality.


title: Goodluck Jonathan

text: The government followed the advice of international experts that claimed the fuel subsidy ($8 billion per year, or 25% of the government annual budget) was not sustainable. Brookings Institution, a think tank, praised the government's move, arguing that the subsidy crowds out other development spending, like education, and that it discourages investment in the country's economic lifeblood, the oil sector. In his book, "My Transition Hours", Goodluck Jonathan said that subsidy was consuming too much of our revenues and the public believed that the sector was highly corrupt. He mentioned that the Minister of Finance Ngozi Okonjo Iweala briefed him about the corrupt practices that a technical committee she had put together discovered. He said that he was alarmed that billions of naira was being lost by the nation through the subsidy regime.


title: Goodluck Jonathan

text: Many prominent Nigerians spoke out against the removal of the subsidy. Former Petroleum Minister Professor Tam David-West spoke out and expressed concern that the planned removal of the fuel subsidy will squeeze the economy, increase inflation, and hurt both businesses and the public. A former military Head of State and a former Minister for Petroleum & Natural Resources, General Muhammadu Buhari, urged Jonathan not to remove the fuel subsidy and to tackle corruption. Yakubu Gowon, another former military Head of State, warned the government that the country's infrastructure should be revived before fuel subsidy removal steps were taken. Former military president Gen. Ibrahim Babangida, joined millions of Nigerians protesting against the removal of the fuel subsidy by the Jonathan administration, saying that the action is ill-timed.


title: Goodluck Jonathan

text: In March 2014, President Jonathan inaugurated the 2014 National Conference. The conference was the first of its kind since the 2005 political reform conference, it had 492 delegates that debated on key socio-political national issues impeding national development.


title: Goodluck Jonathan

text: On 20 July 2014, Patrick Sawyer, a Liberian-American, flew from Monrovia to Murtala Muhammed International Airport in Lagos, with a stopover at Lomé, Togo. He was subsequently described as having appeared to be "terribly ill" when he left Monrovia. Sawyer became violently ill upon arriving at the airport and died five days later. In response, the Nigerian government observed all of Sawyer's contacts for signs of infection and increased surveillance at all entry points to the country.


title: Goodluck Jonathan

text: On 6 August 2014, the Nigerian health minister told reporters: "Yesterday, the first known Nigerian to die of Ebola was recorded. This was one of the nurses that attended to the Liberian. The other five newly confirmed cases are being treated at an isolation ward." The doctor who treated Sawyer, Ameyo Adadevoh, subsequently also died of Ebola. On 22 September 2014, the Nigeria ministry of health announced: "As of today, there is no case of Ebola in Nigeria. All listed contacts who were under surveillance have been followed up for 21 days. "According to the WHO, 20 cases and 8 deaths had been confirmed, along with the imported case, who also died. Four of the dead were health care workers who had cared for Sawyer. In all, 529 contacts had been followed and of that date they had all completed a 21-day mandatory period of surveillance.


title: Goodluck Jonathan

text: In January 2014, Jonathan signed into law the Same Sex Marriage Prohibition Act after it was passed by the Senate and House of Representatives. The law prohibits gay relationships, membership and other involvement in gay societies and organisations and gay marriages. The bill came after international polls showed that 98% of Nigerians did not think homosexuality should be accepted by society, the highest percentage of any country surveyed. Penalties can be up to 14 years in prison for gay marriages and up to 10 years for other violations of the law. Within a short period, the federal police department compiled a list of 168 gay people who would subsequently be jailed. Within days 38 lesbian and gay people had been jailed, with arrests beginning during Christmas. The anti-LGBT bill stipulates that those who withhold the details of LGBT individuals face prison terms of up to five years. His decision and the law itself have been described as controversial, but according to a poll, 92% of Nigerians supported the ban.


title: Goodluck Jonathan

text: Jonathan's administration was heavily criticized for its failure to tackle insecurity. The first major challenge was the October 2010 Independence Day bombing. Okah told the court that President Jonathan and his aides organised the attacks in Abuja in a desperate political strategy to demonise political opponents, including former military head of state General Ibrahim Babangida, and to win popular sympathy ahead of the elections.


title: Goodluck Jonathan

text: On 29 May 2011, a few hours after Goodluck Jonathan was sworn in as president, several bombings purportedly by Boko Haram killed 15 and injured 55. On 16 June 2011, Boko Haram claimed to have conducted the Abuja police headquarters bombing, the first known suicide attack in Nigeria. Two months later the United Nations building in Abuja was bombed, signifying the first time that Boko Haram attacked an international organisation. In December 2011, it carried out attacks in Damaturu killing over a hundred people, subsequently clashing with security forces in December, resulting in at least 68 deaths. Two days later on Christmas Day, Boko Haram attacked several Christian churches with bomb blasts and shootings.


title: Goodluck Jonathan

text: Following the January 2012 Northern Nigeria attacks, which left over hundreds of casualties, Abubakar Shekau, a former deputy of Mohammed Yusuf, appeared in a video posted on YouTube. According to Reuters, Shekau took control of the group after the death of Yusuf in 2009. Authorities had previously believed that Shekau died during the violence in 2009. By early 2012, the group was responsible for over 900 deaths. On 8 March 2012, a small Special Boat Service team and the Nigerian Army attempted to rescue two hostages, Chris McManus and Franco Lamolinara, being held in Nigeria by members of the Boko Haram terrorist organisation loyal to al-Qaeda. The two hostages were killed before or during the rescue attempt. All the hostage takers were reportedly killed.


title: Goodluck Jonathan

text: On 18 March, a bus station was bombed in Kano, with several casualties. In May 2013, Nigerian government forces launched an offensive in the Borno region in an attempt to dislodge Boko Haram fighters after a state of emergency was called on 14 May 2013. The state of emergency, applied to the states of Borno, Yobe, and Adamawa in northeastern Nigeria. The offensive had initial success, but the Boko Haram rebels were able to regain their strength. Although initially offering amnesty, by June 2013 he ordered a 20-year jail term for anyone found to be in support of Boko Haram. In July 2013, Boko Haram massacred 42 students in Yobe, bringing the school year to an early end in the state. On 5 August 2013, Boko Haram launched dual attacks on Bama and Malam Fatori, leaving 35 dead.


title: Goodluck Jonathan

text: On 16 January 2014, it was reported that Jonathan had sacked his military high command in response to their inability to end the Islamist-led insurgency in Northern Nigeria. On 14 April, over 200 schoolgirls in Chibok were kidnapped. A few weeks later in May, a terrorist offensive was launched against the military in Chibok. Many demonstrations called for the government to be more responsive; Jonathan asked that demonstrators focus on blaming Boko Haram itself for the abductions. Jonathan initially denied that there had been any abduction at all, but then later signaled his government would do a prisoner release in exchange for the kidnapped girls. Discussions then took place in Paris with foreign ministers from France, Britain, the United States and Israel, where he agreed no deals should be struck with terrorists. He then called off the exchange at the last minute on 24 May 2014. This reportedly enraged Boko Haram leaders.


title: Goodluck Jonathan

text: In May 2014, two bombs exploded in Jos, resulting in the deaths of at least 118 people and the injury or over 56 others. During the June 2014 Northern Nigeria attacks, a plaza in the capital city was bombed and hundreds of villagers attacked in a two-day killing spree in Kaduna. In November, Boko Haram bombed the city of Kano, attempting to assassinate the Emir Muhammadu Sanusi II. Starting in late 2014, Boko Haram militants attacked several Nigerian towns in the North and captured them. This prompted the Nigerian government to launch an offensive, and with the help of Chad, Niger, and Cameroon, they have recaptured many areas that were formerly under the control of Boko Haram. In late 2014, Boko Haram seized control of Bama, according to the town's residents. In December 2014, it was reported that "people too elderly to flee Gwoza Local Government Area were being rounded up and taken to two schools where the militants opened fire on them." Over 50 elderly people in Bama were killed. A "gory" video was released of insurgents shooting over a hundred civilians in a school dormitory in the town of Bama.


title: Goodluck Jonathan

text: Between 3 and 7 January 2015, Boko Haram attacked the town of Baga and killed up to 2,000 people, perhaps the largest massacre by Boko Haram. On 10 January 2015, a bomb attack took place at the Monday Market in Maiduguri, killing 19 people. The city is considered to be at the heart of the Boko Haram insurgency. In the early hours of 25 January 2015, Boko Haram launched a major assault on the city. On 26 January 2015 CNN reported that the attack on Maiduguri by "hundreds of gunmen" had been repelled, but the nearby town of Monguno was captured by Boko Haram. The Nigerian Army claimed to have successfully repelled another attack on Maiduguri on 31 January 2015. Starting in late January 2015, a coalition of military forces from Nigeria, Chad, Cameroon, and Niger began a counter-insurgency campaign against Boko Haram. On 4 February 2015, the Chad Army killed over 200 Boko Haram militants. Soon afterwards, Boko Haram launched an attack on the Cameroonian town of Fotokol, killing 81 civilians, 13 Chadian soldiers and 6 Cameroonian soldiers.


title: Goodluck Jonathan

text: On 17 February 2015 the Nigerian military retook Monguno in a coordinated air and ground assault. On 7 March 2015, Boko Haram's leader Abubakar Shekau pledged allegiance to the Islamic State of Iraq and the Levant (ISIL) via an audio message posted on the organisation's Twitter account. Nigerian army spokesperson Sami Usman Kukasheka said the pledge was a sign of weakness and that Shekau was like a "drowning man". That same day, five suicide bomb blasts left 54 dead and 143 wounded. On 12 March 2015, ISIL's spokesman Abu Mohammad al-Adnani released an audiotape in which he welcomed the pledge of allegiance, and described it as an expansion of the group's caliphate to West Africa. Following its declaration of loyalty to ISIL, Boko Haram was designated as the group's "West Africa Province" (Islamic State West Africa Province, or ISWAP) while Shekau was appointed as its first vali (governor). Furthermore, ISIL started to support Boko Haram, but also began to interfere in its internal matters. For example, ISIL's central leadership attempted to reduce Boko Haram's brutality toward civilians and internal critics, as Shekau's ideology was "too extreme even for the Islamic State".


title: Goodluck Jonathan

text: On 24 March 2015, residents of Damasak, Nigeria said that Boko Haram had taken more than 400 women and children from the town as they fled from coalition forces. On 27 March 2015, the Nigerian army captured Gwoza, which was believed to be the location of Boko Haram headquarters. On election day, 28 March 2015, Boko Haram extremists killed 41 people, including a legislator, to discourage hundreds from voting. Niger Army soldiers during counter-insurgency operations against Boko Haram in March 2015. In March 2015, Boko Haram lost control of the Northern Nigerian towns of Bama and Gwoza (believed to be their headquarters) to the Nigerian Army. The Nigerian authorities said that they had taken back 11 of the 14 districts previously controlled by Boko Haram. In April 2016, four Boko Haram camps in the Sambisa Forest were overrun by the Nigerian military who freed nearly 300 females. Boko Haram forces were believed to have retreated to the Mandara Mountains, along the Cameroon–Nigeria border. On 16 March 2015, the Nigerian army said that it had recaptured Bama. On 27 March 2015, the day before the Nigerian presidential election, the Nigerian Army announced that it had recaptured the town of Gwoza from Boko Haram.


title: Goodluck Jonathan

text: By April 2015, the Nigerian military was reported to have retaken most of the areas previously controlled by Boko Haram in Northeastern Nigeria, except for the Sambisa Forest. In May 2015, the Nigerian military announced that they had released about 700 women from camps in Sambisa Forest.


title: Goodluck Jonathan

text: Jonathan believed the APC's popularity was inflated, having made his view clear in an interview with The Cable, Nigeria's Independent Online Newspaper in 2015—just two days to the general elections. Jonathan said "I don’t think Nigerians will make the mistake of voting for Buhari. Gen. Buhari, with due respect, is not the right option for Nigeria at this time. It is a gamble that is not worth taking. I may not be perfect as nobody is perfect. But I believe that come Saturday, the majority of Nigerian voters will choose me as the best candidate to lead the nation forward."


title: Goodluck Jonathan

text: On 31 March 2015, Jonathan conceded the election to challenger Muhammadu Buhari, who was sworn in to succeed him on 29 May 2015. Jonathan said in a statement he issued on 31 March 2015 that "Nobody’s ambition is worth the blood of any Nigerian."


title: Goodluck Jonathan

text: It was alleged that Jonathan has expressed interest to stand for the 2023 Nigeria presidential election under the All People's party (APC). To achieve this, the APC primary nomination form have been picked up for him by his supporters, which was debunked by his media aide Ikechukwu Eze.


title: Goodluck Jonathan

text: Since leaving office, Jonathan has continued to defend his administration. In 2019, he was appointed as the honorary special advisor to the Bayelsa Education Trust Fund board. In June 2019, Goodluck Jonathan was named chairperson of the newly inaugurated International Summit Council for Peace. In July 2020, Jonathan was appointed special envoy of the Economic Community of West African States (ECOWAS); to lead mediation talks during the 2020 Malian protests.


title: Goodluck Jonathan

text: Jonathan and his wife, Dame Patience Jonathan, have two children, Ariwera (son) and Aruabai (daughter).


title: Goodluck Jonathan

text: In 2007, Jonathan declared his assets worth a total of ₦295,304,420 (then equivalent to US$8,569,662).


title: Aestheticism

text: Aestheticism (also the Aesthetic movement) was an art movement in the late 19th century which privileged the aesthetic value of literature, music and the arts over their socio-political functions. According to Aestheticism, art should be produced to be beautiful, rather than to serve a moral, allegorical, or other didactic purpose, a sentiment exemplified by the slogan "art for art's sake." Aestheticism originated in 1860s England with a radical group of artists and designers, including William Morris and Dante Gabriel Rossetti. It flourished in the 1870s and 1880s, gaining prominence and the support of notable writers such as Walter Pater and Oscar Wilde.


title: Aestheticism

text: Aestheticism challenged the values of mainstream Victorian culture, as many Victorians believed that literature and art fulfilled important ethical roles. Writing in "The Guardian", Fiona McCarthy states that "the aesthetic movement stood in stark and sometimes shocking contrast to the crass materialism of Britain in the 19th century."


title: Aestheticism

text: Aestheticism was named by the critic Walter Hamilton in "The Aesthetic Movement in England" in 1882. By the 1890s, decadence, a term with origins in common with aestheticism, was in use across Europe.


title: Aestheticism

text: Aestheticism has its roots in German Romanticism. Though the term "aesthetic" derives from Greek, Alexander Gottlieb Baumgarten's "Aesthetica" (1750) made important use of it in German before Immanuel Kant incorporated it into his philosophy in the "Critique of Judgment" (1790). Kant, in turn, influenced Friedrich Schiller's "Aesthetic Letters" (1794) and his concept of art as "Spiel" (Play): "Man is never so serious as when he plays; man is wholly man only when he plays". In the "Letters", Schiller proclaimed salvation through art:Man has lost his dignity, but Art has saved it, and preserved it for him in expressive marbles. Truth still lives in fiction, and from the copy the original will be restored.These ideas were imported to the English-speaking world largely through the efforts of Thomas Carlyle, whose "Life of Friedrich Schiller" (1825), "Critical and Miscellaneous Essays" and "Sartor Resartus" (1833–34) introduced and advocated aestheticism while also, if not marking the earliest use of the word "aesthetic" in the English language, certainly popularising it. Ruth apRoberts declared him the "apostle of aesthetics in England, 1825-27", in recognition of his pioneering influence on the subsequent development of the Aesthetic Movement.


title: Aestheticism

text: The British decadent writers were much influenced by the Oxford professor Walter Pater and his essays published during 1867–68, in which he stated that life had to be lived intensely, with an ideal of beauty. His text "Studies in the History of the Renaissance" (1873) was very well regarded by art-oriented young men of the late 19th century. Writers of the Decadent movement used the slogan "Art for Art's Sake" ("L'art pour l'art"), the origin of which is debated. Some claim that it was invented by the philosopher Victor Cousin, although Angela Leighton in the publication "On Form: Poetry, Aestheticism and the Legacy of a Word" (2007) notes that the phrase was used by Benjamin Constant as early as 1804. It is generally accepted to have been promoted by Théophile Gautier in France, who interpreted the phrase to suggest that there was not any real association between art and morality.


title: Aestheticism

text: The artists and writers of Aesthetic style tended to profess that the Arts should provide refined sensuous pleasure, rather than convey moral or sentimental messages. As a consequence, they did not accept John Ruskin, Matthew Arnold, and George MacDonald's conception of art as something moral or useful, "Art for truth's sake". Instead, they believed that Art did not have any didactic purpose; it only needed to be beautiful. The Aesthetes developed a cult of beauty, which they considered the basic factor of art. Life should copy Art, they asserted. They considered nature as crude and lacking in design when compared to art. The main characteristics of the style were: suggestion rather than statement, sensuality, great use of symbols, and synaesthetic/Ideasthetic effects—that is, correspondence between words, colours and music. Music was used to establish mood.


title: Aestheticism

text: Predecessors of the Aesthetes included John Keats and Percy Bysshe Shelley, and some of the Pre-Raphaelites who themselves were a legacy of the Romantic spirit. There are a few significant continuities between the Pre-Raphaelite philosophy and that of the Aesthetes: Dedication to the idea of ‘Art for Art’s Sake’; admiration of, and constant striving for, beauty; escapism through visual and literary arts; craftsmanship that is both careful and self-conscious; mutual interest in merging the arts of various media. This final idea is promoted in the poem "L’Art" by Théophile Gautier, who compared the poet to the sculptor and painter. Dante Gabriel Rossetti and Edward Burne-Jones are most strongly associated with Aestheticism. However, their approach to Aestheticism did not share the creed of ‘Art for Art’s Sake’ but rather “a spirited reassertion of those principles of colour, beauty, love, and cleanness that the drab, agitated, discouraging world of the mid-nineteenth century needed so much.” This reassertion of beauty in a drab world also connects to Pre-Raphaelite escapism in art and poetry.


title: Aestheticism

text: In Britain the best representatives were Oscar Wilde, Algernon Charles Swinburne (both influenced by the French Symbolists), James McNeill Whistler and Dante Gabriel Rossetti. These writers and their style were satirised by Gilbert and Sullivan's comic opera "Patience" and other works, such as F. C. Burnand's drama "The Colonel", and in comic magazines such as "Punch," particularly in works by George Du Maurier.


title: Aestheticism

text: Compton Mackenzie's novel "Sinister Street" makes use of the type as a phase through which the protagonist passes as he is influenced by older, decadent individuals. The novels of Evelyn Waugh, who was a young participant of aesthete society at Oxford, describe the aesthetes mostly satirically, but also as a former participant. Some names associated with this assemblage are Robert Byron, Evelyn Waugh, Harold Acton, Nancy Mitford, A.E. Housman and Anthony Powell.


title: Aestheticism

text: Artists associated with the Aesthetic style include Simeon Solomon, James McNeill Whistler, Dante Gabriel Rossetti, Albert Joseph Moore, GF Watts and Aubrey Beardsley. Although the work of Edward Burne-Jones was exhibited at the Grosvenor Gallery which promoted the movement, it is narrative and conveys moral or sentimental messages hence falling outside the movement's purported programme.


title: Aestheticism

text: According to Christopher Dresser, the primary element of decorative art is utility. The maxim "art for art's sake," identifying art or beauty as the primary element in other branches of the Aesthetic Movement, especially fine art, cannot apply in this context. That is, decorative art must first have utility, but may also be beautiful. However, according to Michael Shindler, the decorative art branch of the Aesthetic Movement, was less the utilitarian cousin of Aestheticism's main 'pure' branch, and more the very means by which aesthetes exercised their fundamental design strategy. Like contemporary art, Shindler writes that aestheticism was born of "the conundrum of constituting one’s life in relation to an exterior work" and that it "attempted to overcome" this problem "by subsuming artists within their work in the hope of yielding—more than mere objects—lives which could be living artworks." Thus, "beautiful things became the sensuous set pieces of a drama in which artists were not like their forebears a sort of crew of anonymous stagehands, but stars. Consequently, aesthetes made idols of portraits, prayers of poems, altars of writing desks, chapels of dining rooms, and fallen angels of their fellow men."


title: Aestheticism

text: Government Schools of Design were founded from 1837 onwards in order to improve the design of British goods. Following the Great Exhibition of 1851 efforts were intensified and oriental objects were purchased for the schools teaching collections. Owen Jones, architect and orientalist, was requested to set out key principles of design and these became not only the basis of the schools teaching but also the propositions which preface "The Grammar of Ornament" (1856), which is still regarded as the finest systematic study or practical sourcebook of historic world ornament.


title: Aestheticism

text: Jones identified the need for a new and modern style that would meet the requirements of the modern world, rather than the continual re-cycling of historic styles, but saw no reason to reject the lessons of the past. Christopher Dresser, a student and later Professor at the school worked with Owen Jones on "The Grammar of Ornament", as well as on the 1863 decoration of the oriental courts (Chinese, Japanese, and Indian) at the South Kensington Museum (now the Victoria and Albert Museum), advanced the search for a new style with his two publications "The Art of Decorative Design" 1862, and "Principles of Design" 1873.


title: Aestheticism

text: Production of Aesthetic style furniture was limited to approximately the late 19th century. Aesthetic style furniture is characterized by several common themes:


title: Aestheticism

text: Ebonized furniture means that the wood is painted or stained to a black ebony finish. The furniture is sometimes completely ebony-colored. More often however, there is gilding added to the carved surfaces of the feathers or stylized flowers that adorn the furniture.


title: Aestheticism

text: As aesthetic movement decor was similar to the corresponding writing style in that it was about sensuality and nature, nature themes often appear on the furniture. A typical aesthetic feature is the gilded carved flower, or the stylized peacock feather. Colored paintings of birds or flowers are often seen. Non-ebonized aesthetic movement furniture may have realistic-looking three-dimensional-like renditions of birds or flowers carved into the wood.


title: Aestheticism

text: Contrasting with the ebonized-gilt furniture is use of blue and white for porcelain and china. Similar themes of peacock feathers and nature would be used in blue and white tones on dinnerware and other crockery. The blue and white design was also popular on square porcelain tiles. It is reported that Oscar Wilde used aesthetic decorations during his youth. This aspect of the movement was also satirised by "Punch" magazine and in "Patience".


title: Aestheticism

text: In 1882 Oscar Wilde visited Canada, where he toured the town of Woodstock, Ontario and gave a lecture on May 29 titled "The House Beautiful". In this lecture Wilde exposited the principles of the Aesthetic Movement in decorative and applied design, also known at the time as the "Ornamental Aesthetic" style, according to which local flora and fauna were celebrated as beautiful and textured, layered ceilings were popular. An example of this can be seen in Annandale National Historic Site, located in Tillsonburg, Ontario, Canada. The house was built in 1880 and decorated by Mary Ann Tillson, who happened to attend Oscar Wilde's lecture in Woodstock. Since the Aesthetic Movement was only prevalent in the decorative arts from about 1880 until about 1890, there are not many surviving examples of this particular style but one such example is 18 Stafford Terrace, London, which provides an insight into how the middle classes interpreted its principles. Olana, the home of Frederic Edwin Church in upstate New York, is an important example of exoticism in Aesthetic Movement decorative arts.


title: Aestheticism

text: The aesthetic movement in England became directly involved in advertising, and Pears soap (under advertising pioneer Thomas J. Barratt) recruited English actress and socialite Lillie Langtry—who had been painted by aesthete artists and was also a friend of Oscar Wilde—to promote their products in 1882, making her the first celebrity to endorse a commercial product.


title: Feynman diagram

text: In theoretical physics, a Feynman diagram is a pictorial representation of the mathematical expressions describing the behavior and interaction of subatomic particles. The scheme is named after American physicist Richard Feynman, who introduced the diagrams in 1948. The interaction of subatomic particles can be complex and difficult to understand; Feynman diagrams give a simple visualization of what would otherwise be an arcane and abstract formula. According to David Kaiser, "Since the middle of the 20th century, theoretical physicists have increasingly turned to this tool to help them undertake critical calculations. Feynman diagrams have revolutionized nearly every aspect of theoretical physics." While the diagrams are applied primarily to quantum field theory, they can also be used in other fields, such as solid-state theory. Frank Wilczek wrote that the calculations that won him the 2004 Nobel Prize in Physics "would have been literally unthinkable without Feynman diagrams, as would [Wilczek's] calculations that established a route to production and observation of the Higgs particle."


title: Feynman diagram

text: Feynman used Ernst Stueckelberg's interpretation of the positron as if it were an electron moving backward in time. Thus, antiparticles are represented as moving backward along the time axis in Feynman diagrams.


title: Feynman diagram

text: The calculation of probability amplitudes in theoretical particle physics requires the use of rather large and complicated integrals over a large number of variables. Feynman diagrams can represent these integrals graphically.


title: Feynman diagram

text: A Feynman diagram is a graphical representation of a perturbative contribution to the transition amplitude or correlation function of a quantum mechanical or statistical field theory. Within the canonical formulation of quantum field theory, a Feynman diagram represents a term in the Wick's expansion of the perturbative -matrix. Alternatively, the path integral formulation of quantum field theory represents the transition amplitude as a weighted sum of all possible histories of the system from the initial to the final state, in terms of either particles or fields. The transition amplitude is then given as the matrix element of the -matrix between the initial and final states of the quantum system.


title: Feynman diagram

text: When calculating scattering cross-sections in particle physics, the interaction between particles can be described by starting from a free field that describes the incoming and outgoing particles, and including an interaction Hamiltonian to describe how the particles deflect one another. The amplitude for scattering is the sum of each possible interaction history over all possible intermediate particle states. The number of times the interaction Hamiltonian acts is the order of the perturbation expansion, and the time-dependent perturbation theory for fields is known as the Dyson series. When the intermediate states at intermediate times are energy eigenstates (collections of particles with a definite momentum) the series is called old-fashioned perturbation theory (or time-dependent/time-ordered perturbation theory).


title: Feynman diagram

text: The Dyson series can be alternatively rewritten as a sum over Feynman diagrams, where at each vertex both the energy and momentum are conserved, but where the length of the energy-momentum four-vector is not necessarily equal to the mass, i.e. the intermediate particles are so-called off-shell. The Feynman diagrams are much easier to keep track of than "old-fashioned" terms, because the old-fashioned way treats the particle and antiparticle contributions as separate. Each Feynman diagram is the sum of exponentially many old-fashioned terms, because each internal line can separately represent either a particle or an antiparticle. In a non-relativistic theory, there are no antiparticles and there is no doubling, so each Feynman diagram includes only one term.


title: Feynman diagram

text: Feynman gave a prescription for calculating the amplitude (the Feynman rules, below) for any given diagram from a field theory Lagrangian. Each internal line corresponds to a factor of the virtual particle's propagator; each vertex where lines meet gives a factor derived from an interaction term in the Lagrangian, and incoming and outgoing lines carry an energy, momentum, and spin.


title: Feynman diagram

text: In addition to their value as a mathematical tool, Feynman diagrams provide deep physical insight into the nature of particle interactions. Particles interact in every way available; in fact, intermediate virtual particles are allowed to propagate faster than light. The probability of each final state is then obtained by summing over all such possibilities. This is closely tied to the functional integral formulation of quantum mechanics, also invented by Feynman—see path integral formulation.


title: Feynman diagram

text: The naïve application of such calculations often produces diagrams whose amplitudes are infinite, because the short-distance particle interactions require a careful limiting procedure, to include particle self-interactions. The technique of renormalization, suggested by Ernst Stueckelberg and Hans Bethe and implemented by Dyson, Feynman, Schwinger, and Tomonaga compensates for this effect and eliminates the troublesome infinities. After renormalization, calculations using Feynman diagrams match experimental results with very high accuracy.


title: Feynman diagram

text: Feynman diagram and path integral methods are also used in statistical mechanics and can even be applied to classical mechanics.


title: Feynman diagram

text: Murray Gell-Mann always referred to Feynman diagrams as Stueckelberg diagrams, after a Swiss physicist, Ernst Stueckelberg, who devised a similar notation many years earlier. Stueckelberg was motivated by the need for a manifestly covariant formalism for quantum field theory, but did not provide as automated a way to handle symmetry factors and loops, although he was first to find the correct physical interpretation in terms of forward and backward in time particle paths, all without the path-integral.


title: Feynman diagram

text: Historically, as a book-keeping device of covariant perturbation theory, the graphs were called Feynman–Dyson diagrams or Dyson graphs, because the path integral was unfamiliar when they were introduced, and Freeman Dyson's derivation from old-fashioned perturbation theory borrowed from the perturbative expansions in statistical mechanics was easier to follow for physicists trained in earlier methods. Feynman had to lobby hard for the diagrams, which confused the establishment physicists trained in equations and graphs.


title: Feynman diagram

text: In their presentations of fundamental interactions, written from the particle physics perspective, Gerard 't Hooft and Martinus Veltman gave good arguments for taking the original, non-regularized Feynman diagrams as the most succinct representation of our present knowledge about the physics of quantum scattering of fundamental particles. Their motivations are consistent with the convictions of James Daniel Bjorken and Sidney Drell:


title: Feynman diagram

text: The Feynman graphs and rules of calculation summarize quantum field theory in a form in close contact with the experimental numbers one wants to understand. Although the statement of the theory in terms of graphs may imply perturbation theory, use of graphical methods in the many-body problem shows that this formalism is flexible enough to deal with phenomena of nonperturbative characters ... Some modification of the Feynman rules of calculation may well outlive the elaborate mathematical structure of local canonical quantum field theory ...


title: Feynman diagram

text: Currently, there are no opposing opinions. In quantum field theories the Feynman diagrams are obtained from a Lagrangian by Feynman rules.


title: Feynman diagram

text: Dimensional regularization is a method for regularizing integrals in the evaluation of Feynman diagrams; it assigns values to them that are meromorphic functions of an auxiliary complex parameter , called the dimension. Dimensional regularization writes a Feynman integral as an integral depending on the spacetime dimension and spacetime points.


title: Feynman diagram

text: A Feynman diagram is a representation of quantum field theory processes in terms of particle interactions. The particles are represented by the lines of the diagram, which can be squiggly or straight, with an arrow or without, depending on the type of particle. A point where lines connect to other lines is a "vertex", and this is where the particles meet and interact: by emitting or absorbing new particles, deflecting one another, or changing type.


title: Feynman diagram

text: There are three different types of lines: "internal lines" connect two vertices, "incoming lines" extend from "the past" to a vertex and represent an initial state, and "outgoing lines" extend from a vertex to "the future" and represent the final state (the latter two are also known as "external lines"). Traditionally, the bottom of the diagram is the past and the top the future; other times, the past is to the left and the future to the right. When calculating correlation functions instead of scattering amplitudes, there is no past and future and all the lines are internal. The particles then begin and end on little x's, which represent the positions of the operators whose correlation is being calculated.


title: Feynman diagram

text: Feynman diagrams are a pictorial representation of a contribution to the total amplitude for a process that can happen in several different ways. When a group of incoming particles are to scatter off each other, the process can be thought of as one where the particles travel over all possible paths, including paths that go backward in time.


title: Feynman diagram

text: Feynman diagrams are often confused with spacetime diagrams and bubble chamber images because they all describe particle scattering. Feynman diagrams are graphs that represent the interaction of particles rather than the physical position of the particle during a scattering process. Unlike a bubble chamber picture, only the sum of all the Feynman diagrams represent any given particle interaction; particles do not choose a particular diagram each time they interact. The law of summation is in accord with the principle of superposition—every diagram contributes to the total amplitude for the process.


title: Feynman diagram

text: A Feynman diagram represents a perturbative contribution to the amplitude of a quantum transition from some initial quantum state to some final quantum state.


title: Feynman diagram

text: For example, in the process of electron-positron annihilation the initial state is one electron and one positron, the final state: two photons.


title: Feynman diagram

text: The initial state is often assumed to be at the left of the diagram and the final state at the right (although other conventions are also used quite often).


title: Feynman diagram

text: The particles in the initial state are depicted by lines sticking out in the direction of the initial state (e.g., to the left), the particles in the final state are represented by lines sticking out in the direction of the final state (e.g., to the right).


title: Feynman diagram

text: In QED there are two types of particles: matter particles such as electrons or positrons (called fermions) and exchange particles (called gauge bosons). They are represented in Feynman diagrams as follows:


title: Feynman diagram

text: In QED a vertex always has three lines attached to it: one bosonic line, one fermionic line with arrow toward the vertex, and one fermionic line with arrow away from the vertex.


title: Feynman diagram

text: The vertices might be connected by a bosonic or fermionic propagator. A bosonic propagator is represented by a wavy line connecting two vertices (•~•). A fermionic propagator is represented by a solid line (with an arrow in one or another direction) connecting two vertices, (•←•).


title: Feynman diagram

text: The number of vertices gives the order of the term in the perturbation series expansion of the transition amplitude.


title: Feynman diagram

text: In the initial state (at the bottom; early time) there is one electron (e) and one positron (e) and in the final state (at the top; late time) there are two photons (γ).


title: Feynman diagram

text: The probability amplitude for a transition of a quantum system (between asymptotically free states) from the initial state to the final state is given by the matrix element


title: Feynman diagram

text: where is the interaction Hamiltonian and signifies the time-ordered product of operators. Dyson's formula expands the time-ordered matrix exponential into a perturbation series in the powers of the interaction Hamiltonian density,


title: Feynman diagram

text: A Feynman diagram is a graphical representation of a single summand in the Wick's expansion of the time-ordered product in the th-order term of the Dyson series of the -matrix,


title: Feynman diagram

text: where signifies the normal-ordered product of the operators and (±) takes care of the possible sign change when commuting the fermionic operators to bring them together for a contraction (a propagator) and represents all possible contractions.


title: Feynman diagram

text: The diagrams are drawn according to the Feynman rules, which depend upon the interaction Lagrangian. For the QED interaction Lagrangian


title: Feynman diagram

text: describing the interaction of a fermionic field with a bosonic gauge field , the Feynman rules can be formulated in coordinate space as follows:


title: Feynman diagram

text: is the electromagnetic contraction (propagator) in the Feynman gauge. This term is represented by the Feynman diagram at the right. This diagram gives contributions to the following processes:


title: Feynman diagram

text: In a path integral, the field Lagrangian, integrated over all possible field histories, defines the probability amplitude to go from one field configuration to another. In order to make sense, the field theory should have a well-defined ground state, and the integral should be performed a little bit rotated into imaginary time, i.e. a Wick rotation. The path integral formalism is completely equivalent to the canonical operator formalism above.


title: Feynman diagram

text: where and are space-like hypersurfaces that define the boundary conditions. The collection of all the on the starting hypersurface give the initial value of the field, analogous to the starting position for a point particle, and the field values at each point of the final hypersurface defines the final field value, which is allowed to vary, giving a different amplitude to end up at different values. This is the field-to-field transition amplitude.


title: Feynman diagram

text: and in the limit that A and B recede to the infinite past and the infinite future, the only contribution that matters is from the ground state (this is only rigorously true if the path-integral is defined slightly rotated into imaginary time). The path integral can be thought of as analogous to a probability distribution, and it is convenient to define it so that multiplying by a constant doesn't change anything:


title: Feynman diagram

text: The normalization factor on the bottom is called the "partition function" for the field, and it coincides with the statistical mechanical partition function at zero temperature when rotated into imaginary time.


title: Feynman diagram

text: The initial-to-final amplitudes are ill-defined if one thinks of the continuum limit right from the beginning, because the fluctuations in the field can become unbounded. So the path-integral can be thought of as on a discrete square lattice, with lattice spacing and the limit should be taken carefully. If the final results do not depend on the shape of the lattice or the value of , then the continuum limit exists.


title: Feynman diagram

text: Here the integration domain is over restricted to a cube of side length , so that large values of are not allowed. It is important to note that the -measure contains the factors of 2 from Fourier transforms, this is the best standard convention for -integrals in QFT. The lattice means that fluctuations at large are not allowed to contribute right away, they only start to contribute in the limit . Sometimes, instead of a lattice, the field modes are just cut off at high values of instead.


title: Feynman diagram

text: It is also convenient from time to time to consider the space-time volume to be finite, so that the modes are also a lattice. This is not strictly as necessary as the space-lattice limit, because interactions in are not localized, but it is convenient for keeping track of the factors in front of the -integrals and the momentum-conserving delta functions that will arise.


title: Feynman diagram

text: where is a pair of nearest lattice neighbors and . The discretization should be thought of as defining what the derivative means.


title: Feynman diagram

text: Now we have the continuum Fourier transform of the original action. In finite volume, the quantity is not infinitesimal, but becomes the volume of a box made by neighboring Fourier modes, or .


title: Feynman diagram

text: In terms of real and imaginary parts, the real part of is an even function of , while the imaginary part is odd. The Fourier transform avoids double-counting, so that it can be written:


title: Feynman diagram

text: Integrating over all different values of is equivalent to integrating over all Fourier modes, because taking a Fourier transform is a unitary linear transformation of field coordinates. When you change coordinates in a multidimensional integral by a linear transformation, the value of the new integral is given by the determinant of the transformation matrix. If


title: Feynman diagram

text: The matrix that changes coordinates from to can be read off from the definition of a Fourier transform.


title: Feynman diagram

text: which is the complex conjugate-transpose, up to factors of 2. On a finite volume lattice, the determinant is nonzero and independent of the field values.


title: Feynman diagram

text: where is the side-length of the box. Each separate factor is an oscillatory Gaussian, and the width of the Gaussian diverges as the volume goes to infinity.


title: Feynman diagram

text: In imaginary time, the "Euclidean action" becomes positive definite, and can be interpreted as a probability distribution. The probability of a field having values is


title: Feynman diagram

text: The expectation value of the field is the statistical expectation value of the field when chosen according to the probability distribution:


title: Feynman diagram

text: Since the probability of is a product, the value of at each separate value of is independently Gaussian distributed. The variance of the Gaussian is , which is formally infinite, but that just means that the fluctuations are unbounded in infinite volume. In any finite volume, the integral is replaced by a discrete sum, and the variance of the integral is .


title: Feynman diagram

text: The path integral defines a probabilistic algorithm to generate a Euclidean scalar field configuration. Randomly pick the real and imaginary parts of each Fourier mode at wavenumber to be a Gaussian random variable with variance . This generates a configuration at random, and the Fourier transform gives . For real scalar fields, the algorithm must generate only one of each pair , and make the second the complex conjugate of the first.


title: Feynman diagram

text: To find any correlation function, generate a field again and again by this procedure, and find the statistical average:


title: Feynman diagram

text: where is the number of configurations, and the sum is of the product of the field values on each configuration. The Euclidean correlation function is just the same as the correlation function in statistics or statistical mechanics. The quantum mechanical correlation functions are an analytic continuation of the Euclidean correlation functions.


title: Feynman diagram

text: For free fields with a quadratic action, the probability distribution is a high-dimensional Gaussian, and the statistical average is given by an explicit formula. But the Monte Carlo method also works well for bosonic interacting field theories where there is no closed form for the correlation functions.


title: Feynman diagram

text: Each mode is independently Gaussian distributed. The expectation of field modes is easy to calculate:


title: Feynman diagram

text: in finite volume , when the two -values coincide, since this is the variance of the Gaussian. In the infinite volume limit,


title: Feynman diagram

text: It is important to emphasize that the delta functions contain factors of 2, so that they cancel out the 2 factors in the measure for integrals.


title: Feynman diagram

text: where is the ordinary one-dimensional Dirac delta function. This convention for delta-functions is not universal—some authors keep the factors of 2 in the delta functions (and in the -integration) explicit.


title: Feynman diagram

text: The form of the propagator can be more easily found by using the equation of motion for the field. From the Lagrangian, the equation of motion is:


title: Feynman diagram

text: Where the derivatives act on , and the identity is true everywhere except when and coincide, and the operator order matters. The form of the singularity can be understood from the canonical commutation relations to be a delta-function. Defining the (Euclidean) "Feynman propagator" as the Fourier transform of the time-ordered two-point function (the one that comes from the path-integral):


title: Feynman diagram

text: If the equations of motion are linear, the propagator will always be the reciprocal of the quadratic-form matrix that defines the free Lagrangian, since this gives the equations of motion. This is also easy to see directly from the path integral. The factor of disappears in the Euclidean theory.


title: Feynman diagram

text: Because each field mode is an independent Gaussian, the expectation values for the product of many field modes obeys "Wick's theorem":


title: Feynman diagram

text: is zero unless the field modes coincide in pairs. This means that it is zero for an odd number of , and for an even number of , it is equal to a contribution from each pair separately, with a delta function.


title: Feynman diagram

text: where the sum is over each partition of the field modes into pairs, and the product is over the pairs. For example,


title: Feynman diagram

text: An interpretation of Wick's theorem is that each field insertion can be thought of as a dangling line, and the expectation value is calculated by linking up the lines in pairs, putting a delta function factor that ensures that the momentum of each partner in the pair is equal, and dividing by the propagator.


title: Feynman diagram

text: There is a subtle point left before Wick's theorem is proved—what if more than two of the formula_49s have the same momentum? If it's an odd number, the integral is zero; negative values cancel with the positive values. But if the number is even, the integral is positive. The previous demonstration assumed that the formula_49s would only match up in pairs.


title: Feynman diagram

text: But the theorem is correct even when arbitrarily many of the formula_49 are equal, and this is a notable property of Gaussian integration:


title: Feynman diagram

text: If Wick's theorem were correct, the higher moments would be given by all possible pairings of a list of different :


title: Feynman diagram

text: where the are all the same variable, the index is just to keep track of the number of ways to pair them. The first can be paired with others, leaving . The next unpaired can be paired with different leaving , and so on. This means that Wick's theorem, uncorrected, says that the expectation value of should be:


title: Feynman diagram

text: and this is in fact the correct answer. So Wick's theorem holds no matter how many of the momenta of the internal variables coincide.


title: Feynman diagram

text: Interactions are represented by higher order contributions, since quadratic contributions are always Gaussian. The simplest interaction is the quartic self-interaction, with an action:


title: Feynman diagram

text: The reason for the combinatorial factor 4! will be clear soon. Writing the action in terms of the lattice (or continuum) Fourier modes:


title: Feynman diagram

text: Where is the free action, whose correlation functions are given by Wick's theorem. The exponential of in the path integral can be expanded in powers of , giving a series of corrections to the free action.


title: Feynman diagram

text: The path integral for the interacting action is then a power series of corrections to the free action. The term represented by should be thought of as four half-lines, one for each factor of . The half-lines meet at a vertex, which contributes a delta-function that ensures that the sum of the momenta are all equal.


title: Feynman diagram

text: To compute a correlation function in the interacting theory, there is a contribution from the terms now. For example, the path-integral for the four-field correlator:


title: Feynman diagram

text: which in the free field was only nonzero when the momenta were equal in pairs, is now nonzero for all values of . The momenta of the insertions can now match up with the momenta of the s in the expansion. The insertions should also be thought of as half-lines, four in this case, which carry a momentum , but one that is not integrated.


title: Feynman diagram

text: The lowest-order contribution comes from the first nontrivial term in the Taylor expansion of the action. Wick's theorem requires that the momenta in the half-lines, the factors in , should match up with the momenta of the external half-lines in pairs. The new contribution is equal to:


title: Feynman diagram

text: The 4! inside is canceled because there are exactly 4! ways to match the half-lines in to the external half-lines. Each of these different ways of matching the half-lines together in pairs contributes exactly once, regardless of the values of , by Wick's theorem.


title: Feynman diagram

text: The expansion of the action in powers of gives a series of terms with progressively higher number of s. The contribution from the term with exactly s is called th order.


title: Feynman diagram

text: By Wick's theorem, each pair of half-lines must be paired together to make a "line", and this line gives a factor of


title: Feynman diagram

text: which multiplies the contribution. This means that the two half-lines that make a line are forced to have equal and opposite momentum. The line itself should be labelled by an arrow, drawn parallel to the line, and labeled by the momentum in the line . The half-line at the tail end of the arrow carries momentum , while the half-line at the head-end carries momentum . If one of the two half-lines is external, this kills the integral over the internal , since it forces the internal to be equal to the external . If both are internal, the integral over remains.


title: Feynman diagram

text: The diagrams that are formed by linking the half-lines in the s with the external half-lines, representing insertions, are the Feynman diagrams of this theory. Each line carries a factor of , the propagator, and either goes from vertex to vertex, or ends at an insertion. If it is internal, it is integrated over. At each vertex, the total incoming is equal to the total outgoing .


title: Feynman diagram

text: The number of ways of making a diagram by joining half-lines into lines almost completely cancels the factorial factors coming from the Taylor series of the exponential and the 4! at each vertex.


title: Feynman diagram

text: A forest diagram is one where all the internal lines have momentum that is completely determined by the external lines and the condition that the incoming and outgoing momentum are equal at each vertex. The contribution of these diagrams is a product of propagators, without any integration. A tree diagram is a connected forest diagram.


title: Feynman diagram

text: An example of a tree diagram is the one where each of four external lines end on an . Another is when three external lines end on an , and the remaining half-line joins up with another , and the remaining half-lines of this run off to external lines. These are all also forest diagrams (as every tree is a forest); an example of a forest that is not a tree is when eight external lines end on two s.


title: Feynman diagram

text: It is easy to verify that in all these cases, the momenta on all the internal lines is determined by the external momenta and the condition of momentum conservation in each vertex.


title: Feynman diagram

text: A diagram that is not a forest diagram is called a "loop" diagram, and an example is one where two lines of an are joined to external lines, while the remaining two lines are joined to each other. The two lines joined to each other can have any momentum at all, since they both enter and leave the same vertex. A more complicated example is one where two s are joined to each other by matching the legs one to the other. This diagram has no external lines at all.


title: Feynman diagram

text: The reason loop diagrams are called loop diagrams is because the number of -integrals that are left undetermined by momentum conservation is equal to the number of independent closed loops in the diagram, where independent loops are counted as in homology theory. The homology is real-valued (actually valued), the value associated with each line is the momentum. The boundary operator takes each line to the sum of the end-vertices with a positive sign at the head and a negative sign at the tail. The condition that the momentum is conserved is exactly the condition that the boundary of the -valued weighted graph is zero.


title: Feynman diagram

text: A set of valid -values can be arbitrarily redefined whenever there is a closed loop. A closed loop is a cyclical path of adjacent vertices that never revisits the same vertex. Such a cycle can be thought of as the boundary of a hypothetical 2-cell. The -labellings of a graph that conserve momentum (i.e. which has zero boundary) up to redefinitions of (i.e. up to boundaries of 2-cells) define the first homology of a graph. The number of independent momenta that are not determined is then equal to the number of independent homology loops. For many graphs, this is equal to the number of loops as counted in the most intuitive way.


title: Feynman diagram

text: The number of ways to form a given Feynman diagram by joining together half-lines is large, and by Wick's theorem, each way of pairing up the half-lines contributes equally. Often, this completely cancels the factorials in the denominator of each term, but the cancellation is sometimes incomplete.


title: Feynman diagram

text: The uncancelled denominator is called the "symmetry factor" of the diagram. The contribution of each diagram to the correlation function must be divided by its symmetry factor.


title: Feynman diagram

text: For example, consider the Feynman diagram formed from two external lines joined to one , and the remaining two half-lines in the joined to each other. There are 4 × 3 ways to join the external half-lines to the , and then there is only one way to join the two remaining lines to each other. The comes divided by , but the number of ways to link up the half lines to make the diagram is only 4 × 3, so the contribution of this diagram is divided by two.


title: Feynman diagram

text: For another example, consider the diagram formed by joining all the half-lines of one to all the half-lines of another . This diagram is called a "vacuum bubble", because it does not link up to any external lines. There are 4! ways to form this diagram, but the denominator includes a 2! (from the expansion of the exponential, there are two s) and two factors of 4!. The contribution is multiplied by = .


title: Feynman diagram

text: Another example is the Feynman diagram formed from two s where each links up to two external lines, and the remaining two half-lines of each are joined to each other. The number of ways to link an to two external lines is 4 × 3, and either could link up to either pair, giving an additional factor of 2. The remaining two half-lines in the two s can be linked to each other in two ways, so that the total number of ways to form the diagram is , while the denominator is . The total symmetry factor is 2, and the contribution of this diagram is divided by 2.


title: Feynman diagram

text: The symmetry factor theorem gives the symmetry factor for a general diagram: the contribution of each Feynman diagram must be divided by the order of its group of automorphisms, the number of symmetries that it has.


title: Feynman diagram

text: An automorphism of a Feynman graph is a permutation of the lines and a permutation of the vertices with the following properties:


title: Feynman diagram

text: This theorem has an interpretation in terms of particle-paths: when identical particles are present, the integral over all intermediate particles must not double-count states that differ only by interchanging identical particles.


title: Feynman diagram

text: Proof: To prove this theorem, label all the internal and external lines of a diagram with a unique name. Then form the diagram by linking a half-line to a name and then to the other half line.


title: Feynman diagram

text: Now count the number of ways to form the named diagram. Each permutation of the s gives a different pattern of linking names to half-lines, and this is a factor of . Each permutation of the half-lines in a single gives a factor of 4!. So a named diagram can be formed in exactly as many ways as the denominator of the Feynman expansion.


title: Feynman diagram

text: But the number of unnamed diagrams is smaller than the number of named diagram by the order of the automorphism group of the graph.


title: Feynman diagram

text: Roughly speaking, a Feynman diagram is called "connected" if all vertices and propagator lines are linked by a sequence of vertices and propagators of the diagram itself. If one views it as an undirected graph it is connected. The remarkable relevance of such diagrams in QFTs is due to the fact that they are sufficient to determine the quantum partition function . More precisely, connected Feynman diagrams determine


title: Feynman diagram

text: with constructed from some (arbitrary) Feynman diagram that can be thought to consist of several connected components . If one encounters (identical) copies of a component within the Feynman diagram one has to include a "symmetry factor" . However, in the end each contribution of a Feynman diagram to the partition function has the generic form


title: Feynman diagram

text: To establish the "normalization" one simply calculates all connected "vacuum diagrams", i.e., the diagrams without any "sources" (sometimes referred to as "external legs" of a Feynman diagram).


title: Feynman diagram

text: An immediate consequence of the linked-cluster theorem is that all vacuum bubbles, diagrams without external lines, cancel when calculating correlation functions. A correlation function is given by a ratio of path-integrals:


title: Feynman diagram

text: The top is the sum over all Feynman diagrams, including disconnected diagrams that do not link up to external lines at all. In terms of the connected diagrams, the numerator includes the same contributions of vacuum bubbles as the denominator:


title: Feynman diagram

text: Where the sum over diagrams includes only those diagrams each of whose connected components end on at least one external line. The vacuum bubbles are the same whatever the external lines, and give an overall multiplicative factor. The denominator is the sum over all vacuum bubbles, and dividing gets rid of the second factor.


title: Feynman diagram

text: The vacuum bubbles then are only useful for determining itself, which from the definition of the path integral is equal to:


title: Feynman diagram

text: where is the energy density in the vacuum. Each vacuum bubble contains a factor of zeroing the total at each vertex, and when there are no external lines, this contains a factor of , because the momentum conservation is over-enforced. In finite volume, this factor can be identified as the total volume of space time. Dividing by the volume, the remaining integral for the vacuum bubble has an interpretation: it is a contribution to the energy density of the vacuum.


title: Feynman diagram

text: Correlation functions are the sum of the connected Feynman diagrams, but the formalism treats the connected and disconnected diagrams differently. Internal lines end on vertices, while external lines go off to insertions. Introducing "sources" unifies the formalism, by making new vertices where one line can end.


title: Feynman diagram

text: Sources are external fields, fields that contribute to the action, but are not dynamical variables. A scalar field source is another scalar field that contributes a term to the (Lorentz) Lagrangian:


title: Feynman diagram

text: In the Feynman expansion, this contributes H terms with one half-line ending on a vertex. Lines in a Feynman diagram can now end either on an vertex, or on an vertex, and only one line enters an vertex. The Feynman rule for an vertex is that a line from an with momentum gets a factor of .


title: Feynman diagram

text: The sum of the connected diagrams in the presence of sources includes a term for each connected diagram in the absence of sources, except now the diagrams can end on the source. Traditionally, a source is represented by a little "×" with one line extending out, exactly as an insertion.


title: Feynman diagram

text: where is the connected diagram with external lines carrying momentum as indicated. The sum is over all connected diagrams, as before.


title: Feynman diagram

text: The field is not dynamical, which means that there is no path integral over : is just a parameter in the Lagrangian, which varies from point to point. The path integral for the field is:


title: Feynman diagram

text: and it is a function of the values of at every point. One way to interpret this expression is that it is taking the Fourier transform in field space. If there is a probability density on , the Fourier transform of the probability density is:


title: Feynman diagram

text: The Fourier transform is the expectation of an oscillatory exponential. The path integral in the presence of a source is:


title: Feynman diagram

text: The Fourier transform of a delta-function is a constant, which gives a formal expression for a delta function:


title: Feynman diagram

text: This tells you what a field delta function looks like in a path-integral. For two scalar fields and ,


title: Feynman diagram

text: which integrates over the Fourier transform coordinate, over . This expression is useful for formally changing field coordinates in the path integral, much as a delta function is used to change coordinates in an ordinary multi-dimensional integral.


title: Feynman diagram

text: The partition function is now a function of the field , and the physical partition function is the value when is the zero function:


title: Feynman diagram

text: In Euclidean space, source contributions to the action can still appear with a factor of , so that they still do a Fourier transform.


title: Feynman diagram

text: The field path integral can be extended to the Fermi case, but only if the notion of integration is expanded. A Grassmann integral of a free Fermi field is a high-dimensional determinant or Pfaffian, which defines the new type of Gaussian integration appropriate for Fermi fields.


title: Feynman diagram

text: where is an antisymmetric matrix, is a collection of Grassmann variables, and the is to prevent double-counting (since ).


title: Feynman diagram

text: In matrix notation, where and are Grassmann-valued row vectors, and are Grassmann-valued column vectors, and is a real-valued matrix:


title: Feynman diagram

text: where the last equality is a consequence of the translation invariance of the Grassmann integral. The Grassmann variables are external sources for , and differentiating with respect to pulls down factors of .


title: Feynman diagram

text: again, in a schematic matrix notation. The meaning of the formula above is that the derivative with respect to the appropriate component of and gives the matrix element of . This is exactly analogous to the bosonic path integration formula for a Gaussian integral of a complex bosonic field:


title: Feynman diagram

text: So that the propagator is the inverse of the matrix in the quadratic part of the action in both the Bose and Fermi case.


title: Feynman diagram

text: For real Grassmann fields, for Majorana fermions, the path integral is a Pfaffian times a source quadratic form, and the formulas give the square root of the determinant, just as they do for real Bosonic fields. The propagator is still the inverse of the quadratic part.


title: Feynman diagram

text: formally gives the equations of motion and the anticommutation relations of the Dirac field, just as the Klein Gordon Lagrangian in an ordinary path integral gives the equations of motion and commutation relations of the scalar field. By using the spatial Fourier transform of the Dirac field as a new basis for the Grassmann algebra, the quadratic part of the Dirac action becomes simple to invert:


title: Feynman diagram

text: The propagator is the inverse of the matrix linking and , since different values of do not mix together.


title: Feynman diagram

text: where S is the sign of the permutation that reorders the sequence of and to put the ones that are paired up to make the delta-functions next to each other, with the coming right before the . Since a pair is a commuting element of the Grassmann algebra, it doesn't matter what order the pairs are in. If more than one pair have the same , the integral is zero, and it is easy to check that the sum over pairings gives zero in this case (there are always an even number of them). This is the Grassmann analog of the higher Gaussian moments that completed the Bosonic Wick's theorem earlier.


title: Feynman diagram

text: The rules for spin- Dirac particles are as follows: The propagator is the inverse of the Dirac operator, the lines have arrows just as for a complex scalar field, and the diagram acquires an overall factor of −1 for each closed Fermi loop. If there are an odd number of Fermi loops, the diagram changes sign. Historically, the −1 rule was very difficult for Feynman to discover. He discovered it after a long process of trial and error, since he lacked a proper theory of Grassmann integration.


title: Feynman diagram

text: The rule follows from the observation that the number of Fermi lines at a vertex is always even. Each term in the Lagrangian must always be Bosonic. A Fermi loop is counted by following Fermionic lines until one comes back to the starting point, then removing those lines from the diagram. Repeating this process eventually erases all the Fermionic lines: this is the Euler algorithm to 2-color a graph, which works whenever each vertex has even degree. The number of steps in the Euler algorithm is only equal to the number of independent Fermionic homology cycles in the common special case that all terms in the Lagrangian are exactly quadratic in the Fermi fields, so that each vertex has exactly two Fermionic lines. When there are four-Fermi interactions (like in the Fermi effective theory of the weak nuclear interactions) there are more -integrals than Fermi loops. In this case, the counting rule should apply the Euler algorithm by pairing up the Fermi lines at each vertex into pairs that together form a bosonic factor of the term in the Lagrangian, and when entering a vertex by one line, the algorithm should always leave with the partner line.


title: Feynman diagram

text: To clarify and prove the rule, consider a Feynman diagram formed from vertices, terms in the Lagrangian, with Fermion fields. The full term is Bosonic, it is a commuting element of the Grassmann algebra, so the order in which the vertices appear is not important. The Fermi lines are linked into loops, and when traversing the loop, one can reorder the vertex terms one after the other as one goes around without any sign cost. The exception is when you return to the starting point, and the final half-line must be joined with the unlinked first half-line. This requires one permutation to move the last to go in front of the first , and this gives the sign.


title: Feynman diagram

text: This rule is the only visible effect of the exclusion principle in internal lines. When there are external lines, the amplitudes are antisymmetric when two Fermi insertions for identical particles are interchanged. This is automatic in the source formalism, because the sources for Fermi fields are themselves Grassmann valued.


title: Feynman diagram

text: The quadratic form defining the propagator is non-invertible. The reason is the gauge invariance of the field; adding a gradient to does not change the physics.


title: Feynman diagram

text: To fix this problem, one needs to fix a gauge. The most convenient way is to demand that the divergence of is some function , whose value is random from point to point. It does no harm to integrate over the values of , since it only determines the choice of gauge. This procedure inserts the following factor into the path integral for :


title: Feynman diagram

text: The first factor, the delta function, fixes the gauge. The second factor sums over different values of that are inequivalent gauge fixings. This is simply


title: Feynman diagram

text: The additional contribution from gauge-fixing cancels the second half of the free Lagrangian, giving the Feynman Lagrangian:


title: Feynman diagram

text: which is just like four independent free scalar fields, one for each component of . The Feynman propagator is:


title: Feynman diagram

text: The one difference is that the sign of one propagator is wrong in the Lorentz case: the timelike component has an opposite sign propagator. This means that these particle states have negative norm—they are not physical states. In the case of photons, it is easy to show by diagram methods that these states are not physical—their contribution cancels with longitudinal photons to only leave two physical photon polarization contributions for any value of .


title: Feynman diagram

text: If the averaging over is done with a coefficient different from , the two terms don't cancel completely. This gives a covariant Lagrangian with a coefficient formula_96, which does not affect anything:


title: Feynman diagram

text: To find the Feynman rules for non-Abelian gauge fields, the procedure that performs the gauge fixing must be carefully corrected to account for a change of variables in the path-integral.


title: Feynman diagram

text: To find the form of the determinant, consider first a simple two-dimensional integral of a function that depends only on , not on the angle . Inserting an integral over :


title: Feynman diagram

text: The derivative-factor ensures that popping the delta function in removes the integral. Exchanging the order of integration,


title: Feynman diagram

text: The integral over just gives an overall factor of 2, while the rate of change of with a change in is just , so this exercise reproduces the standard formula for polar integration of a radial function:


title: Feynman diagram

text: The factor in front is the volume of the gauge group, and it contributes a constant, which can be discarded. The remaining integral is over the gauge fixed action.


title: Feynman diagram

text: where is the adjoint valued element of the Lie algebra at every point that performs the infinitesimal gauge transformation. This adds the Faddeev Popov determinant to the action:


title: Feynman diagram

text: The determinant is independent of , so the path-integral over can give the Feynman propagator (or a covariant propagator) by choosing the measure for as in the abelian case. The full gauge fixed action is then the Yang Mills action in Feynman gauge with an additional ghost action:


title: Feynman diagram

text: The diagrams are derived from this action. The propagator for the spin-1 fields has the usual Feynman form. There are vertices of degree 3 with momentum factors whose couplings are the structure constants, and vertices of degree 4 whose couplings are products of structure constants. There are additional ghost loops, which cancel out timelike and longitudinal states in loops.


title: Feynman diagram

text: In the Abelian case, the determinant for covariant gauges does not depend on , so the ghosts do not contribute to the connected diagrams.


title: Feynman diagram

text: Feynman diagrams were originally discovered by Feynman, by trial and error, as a way to represent the contribution to the S-matrix from different classes of particle trajectories.


title: Feynman diagram

text: The meaning of this identity (which is an elementary integration) is made clearer by Fourier transforming to real space.


title: Feynman diagram

text: The contribution at any one value of to the propagator is a Gaussian of width . The total propagation function from 0 to is a weighted sum over all proper times of a normalized Gaussian, the probability of ending up at after a random walk of time .


title: Feynman diagram

text: The Schwinger representation is both useful for making manifest the particle aspect of the propagator, and for symmetrizing denominators of loop diagrams.


title: Feynman diagram

text: The Schwinger representation has an immediate practical application to loop diagrams. For example, for the diagram in the theory formed by joining two s together in two half-lines, and making the remaining lines external, the integral over the internal propagators in the loop is:


title: Feynman diagram

text: Here one line carries momentum and the other . The asymmetry can be fixed by putting everything in the Schwinger representation.


title: Feynman diagram

text: except for the asymmetrical little bit. Defining the variable and , the variable goes from 0 to , while goes from 0 to 1. The variable is the total proper time for the loop, while parametrizes the fraction of the proper time on the top of the loop versus the bottom.


title: Feynman diagram

text: leaving only the -integral. This method, invented by Schwinger but usually attributed to Feynman, is called "combining denominator". Abstractly, it is the elementary identity:


title: Feynman diagram

text: But this form does not provide the physical motivation for introducing ; is the proportion of proper time on one of the legs of the loop.


title: Feynman diagram

text: This form shows that the moment that is more negative than four times the mass of the particle in the loop, which happens in a physical region of Lorentz space, the integral has a cut. This is exactly when the external momentum can create physical particles.


title: Feynman diagram

text: The integral over the Schwinger parameters can be split up as before into an integral over the total proper time and an integral over the fraction of the proper time in all but the first segment of the loop for . The are positive and add up to less than 1, so that the integral is over an -dimensional simplex.


title: Feynman diagram

text: Since the numerator of the integrand is not involved, the same prescription works for any loop, no matter what the spins are carried by the legs. The interpretation of the parameters is that they are the fraction of the total proper time spent on each leg.


title: Feynman diagram

text: The correlation functions of a quantum field theory describe the scattering of particles. The definition of "particle" in relativistic field theory is not self-evident, because if you try to determine the position so that the uncertainty is less than the compton wavelength, the uncertainty in energy is large enough to produce more particles and antiparticles of the same type from the vacuum. This means that the notion of a single-particle state is to some extent incompatible with the notion of an object localized in space.


title: Feynman diagram

text: In the 1930s, Wigner gave a mathematical definition for single-particle states: they are a collection of states that form an irreducible representation of the Poincaré group. Single particle states describe an object with a finite mass, a well defined momentum, and a spin. This definition is fine for protons and neutrons, electrons and photons, but it excludes quarks, which are permanently confined, so the modern point of view is more accommodating: a particle is anything whose interaction can be described in terms of Feynman diagrams, which have an interpretation as a sum over particle trajectories.


title: Feynman diagram

text: A field operator can act to produce a one-particle state from the vacuum, which means that the field operator produces a superposition of Wigner particle states. In the free field theory, the field produces one particle states only. But when there are interactions, the field operator can also produce 3-particle, 5-particle (if there is no +/− symmetry also 2, 4, 6 particle) states too. To compute the scattering amplitude for single particle states only requires a careful limit, sending the fields to infinity and integrating over space to get rid of the higher-order corrections.


title: Feynman diagram

text: The relation between scattering and correlation functions is the LSZ-theorem: The scattering amplitude for particles to go to particles in a scattering event is the given by the sum of the Feynman diagrams that go into the correlation function for field insertions, leaving out the propagators for the external legs.


title: Feynman diagram

text: For example, for the interaction of the previous section, the order contribution to the (Lorentz) correlation function is:


title: Feynman diagram

text: Stripping off the external propagators, that is, removing the factors of , gives the invariant scattering amplitude :


title: Feynman diagram

text: which is a constant, independent of the incoming and outgoing momentum. The interpretation of the scattering amplitude is that the sum of over all possible final states is the probability for the scattering event. The normalization of the single-particle states must be chosen carefully, however, to ensure that is a relativistic invariant.


title: Feynman diagram

text: Non-relativistic single particle states are labeled by the momentum , and they are chosen to have the same norm at every value of . This is because the nonrelativistic unit operator on single particle states is:


title: Feynman diagram

text: In relativity, the integral over the -states for a particle of mass m integrates over a hyperbola in space defined by the energy–momentum relation:


title: Feynman diagram

text: If the integral weighs each point equally, the measure is not Lorentz-invariant. The invariant measure integrates over all values of and , restricting to the hyperbola with a Lorentz-invariant delta function:


title: Feynman diagram

text: The invariant amplitude is then the probability amplitude for relativistically normalized incoming states to become relativistically normalized outgoing states.


title: Feynman diagram

text: For nonrelativistic values of , the relativistic normalization is the same as the nonrelativistic normalization (up to a constant factor ). In this limit, the invariant scattering amplitude is still constant. The particles created by the field scatter in all directions with equal amplitude.


title: Feynman diagram

text: The nonrelativistic potential, which scatters in all directions with an equal amplitude (in the Born approximation), is one whose Fourier transform is constant—a delta-function potential. The lowest order scattering of the theory reveals the non-relativistic interpretation of this theory—it describes a collection of particles with a delta-function repulsion. Two such particles have an aversion to occupying the same point at the same time.


title: Feynman diagram

text: Thinking of Feynman diagrams as a perturbation series, nonperturbative effects like tunneling do not show up, because any effect that goes to zero faster than any polynomial does not affect the Taylor series. Even bound states are absent, since at any finite order particles are only exchanged a finite number of times, and to make a bound state, the binding force must last forever.


title: Feynman diagram

text: But this point of view is misleading, because the diagrams not only describe scattering, but they also are a representation of the short-distance field theory correlations. They encode not only asymptotic processes like particle scattering, they also describe the multiplication rules for fields, the operator product expansion. Nonperturbative tunneling processes involve field configurations that on average get big when the coupling constant gets small, but each configuration is a coherent superposition of particles whose local interactions are described by Feynman diagrams. When the coupling is small, these become collective processes that involve large numbers of particles, but where the interactions between each of the particles is simple. (The perturbation series of any interacting quantum field theory has zero radius of convergence, complicating the limit of the infinite series of diagrams needed (in the limit of vanishing coupling) to describe such field configurations.)


title: Feynman diagram

text: This means that nonperturbative effects show up asymptotically in resummations of infinite classes of diagrams, and these diagrams can be locally simple. The graphs determine the local equations of motion, while the allowed large-scale configurations describe non-perturbative physics. But because Feynman propagators are nonlocal in time, translating a field process to a coherent particle language is not completely intuitive, and has only been explicitly worked out in certain special cases. In the case of nonrelativistic bound states, the Bethe–Salpeter equation describes the class of diagrams to include to describe a relativistic atom. For quantum chromodynamics, the Shifman–Vainshtein–Zakharov sum rules describe non-perturbatively excited long-wavelength field modes in particle language, but only in a phenomenological way.


title: Feynman diagram

text: The number of Feynman diagrams at high orders of perturbation theory is very large, because there are as many diagrams as there are graphs with a given number of nodes. Nonperturbative effects leave a signature on the way in which the number of diagrams and resummations diverge at high order. It is only because non-perturbative effects appear in hidden form in diagrams that it was possible to analyze nonperturbative effects in string theory, where in many cases a Feynman description is the only one available.


title: Vatnik (slang)

text: Vatnik or vatnyk () is a pejorative, used in Russia and other post-Soviet states based on an Internet meme that was introduced in 2011 by Anton Chadskiy, which denotes a steadfast jingoistic follower of propaganda from the Russian Government.


title: Vatnik (slang)

text: The use of the word originates in the Internet meme, first spread by Chadskiy on VKontakte and later used in Russia, Ukraine, then in other post-Soviet states. Its meaning refers to the original cartoon, which depicts a character made from the material of a padded cotton wool jacket and bearing a black eye which is used to disparage someone as a blindly patriotic and jingoist who pushes the conventional views presented in Russian government media as well as those of Russian web brigades. "Put simply, the vatnik is representative of a certain archetypical Russian who … supports the regime out of fear, hatred of others, or most often a combination of both."


title: Vatnik (slang)

text: The meme was created by the Russian artist Anton Chadskiy under the pseudonym "Jedem das Seine". His associated picture of an anthropomorphic square-shaped quilted jacket similar to the title character of "SpongeBob SquarePants" was posted on VK for the first time on September 9, 2011. In 2012, the meme became widely popular on the Internet. Chadskiy created the group for the character on VK called "RASHKA - THE SQUARE VATNIK". "Rashka" is a derogatory nickname for Russia, derived from the English pronunciation of the country's name with the Russian -k diminutive suffix attached.


title: Vatnik (slang)

text: Chadskiy's original drawing has been reproduced and modified many times. Features that are consistently included are gray color, a red nose (from drinking vodka), and a black eye (presumably from a fistfight with another vatnik). The meme became much more widespread in society after the Russian military intervention in Ukraine started in 2014.


title: Vatnik (slang)

text: In early 2015, Anton Chadskiy reported that he was forced to leave Russia in November 2014 because he feared political persecution by the government. He was living in Kyiv and planning to move to Berlin at the time.


title: BioShock 2

text: BioShock 2 is a first-person shooter video game developed by 2K Marin and published by 2K Games. It was released worldwide for PlayStation 3, Windows, and Xbox 360 on February 9, 2010; Feral Interactive released an OS X version on March 30, 2012. The game takes place in the dystopian underwater city of Rapture, eight years after the events of "BioShock". In the single-player campaign, players control the armored protagonist Subject Delta as he fights through Splicers—the psychotic human population of the city—using weapons and an array of genetic modifications. The game includes a story-driven multiplayer mode that takes place before the events of "BioShock", during Rapture's civil war.


title: BioShock 2

text: After the success of "BioShock," 2K Games formed a new studio, 2K Marin, to create the sequel. 2K Australia, Arkane Studios, and Digital Extremes provided additional support. The developers focused on improving gameplay elements from the first game, and return to the Rapture setting to explore a new perspective of the city. The story received major changes throughout development. Garry Schyman, who composed "BioShock"s soundtrack, returned for the sequel; he expanded the game's sonic palette to include more blues and religious music to parallel its themes.