弦論是將結合量子力學和廣義相對論成萬有理論的理論物理學。 弦論已得到數十年的深入研究，在歷史上出現了兩次超弦革命。在眾多研究人員共同努力下，弦理論早已與量子引力、粒子物理和凝聚態物理、宇宙學和純數學融匯貫通，發展成了一個廣泛多樣的學科。 S 矩陣理論 維爾納海森堡 1943 年一項研究計劃說弦理論是 S 矩陣理論的產物。Rickles 2014 p 28 n 17 Smatrix theory had enough time to spawn string theory 約翰惠勒於 1937 年引入 S 矩陣後，John Archibald Wheeler On the Mathematical Description of Light Nuclei by the Method of Resonating Group Structure Phys Rev 52 11071122 1937 從 1950 年後期到 60 年代，許多著名的理論家都接受並提倡。但該領域在 70 年代中期被邊緣化並被丟棄 Rickles 2014 p 113：An unfortunate for string theory series of events terminated the growing popularity that string theory was enjoying in the early 1970s 並在 80 年代被量子色動力學取代了。Rickles 2014 p 4 1943 年，維爾納海森堡提出了 S 矩陣理論作為粒子相互作用的原理。W Heisenberg Die beobachtbaren Größenin der Theorie der Elementarteilche In Zeitschrift für Physik 120 7 July 1943 pp 51353 The theory presented a radical rethinking of the foundations of physical laws By the 1940s it had become clear that the proton and the neutron were not pointlike particles like the electron Their magnetic moment differed greatly from that of a pointlike spin½ charged particle too much to attribute the difference to a small perturbation Their interactions were so strong that they scattered like a small sphere not like a point Heisenberg proposed that the strongly interacting particles were in fact extended objects and because there are difficulties of principle with extended relativistic particles he proposed that the notion of a spacetime point broke down at nuclear scales Without space and time it becomes difficult to formulate a physical theory Heisenberg proposed a solution to this problem focusing on the observable quantitiesthose things measurable by experiments An experiment only sees a microscopic quantity if it can be transferred by a series of events to the classical devices that surround the experimental chamber The objects that fly to infinity are stable particles in quantum superpositions of different momentum states Heisenberg proposed that even when space and time are unreliable the notion of momentum state which is defined far away from the experimental chamber still works The physical quantity he proposed as fundamental is the quantum mechanical amplitude for a group of incoming particles to turn into a group of outgoing particles and he did not admit that there were any steps in between The Smatrix is the quantity that describes how a collection of incoming particles turn into outgoing ones Heisenberg proposed to study the Smatrix directly without any assumptions about spacetime structure But when transitions from the farpast to the farfuture occur in one step with no intermediate steps it becomes difficult to calculate anything In quantum field theory the intermediate steps are the fluctuations of fields or equivalently the fluctuations of virtual particles In this proposed Smatrix theory there are no local quantities at all Heisenberg proposed to use unitarity to determine the Smatrix In all conceivable situations the sum of the squares of the amplitudes must equal 1 This property can determine the amplitude in a quantum field theory order by order in a perturbation series once the basic interactions are given and in many quantum field theories the amplitudes grow too fast at high energies to make a unitary Smatrix But without extra assumptions on the highenergy behavior unitarity is not enough to determine the scattering and the proposal was ignored for many years Heisenbergs proposal was revived in 1956 when Murray GellMann recognized that dispersion relationslike those discovered by Hendrik Kramers and Ralph Kronig in the 1920s see KramersKronig relationsallow the formulation of a notion of causality a notion that events in the future would not influence events in the past even when the microscopic notion of past and future are not clearly defined He also recognized that these relations might be useful in computing observables for the case of strong interaction physicsGellMann M G 1956 Dispersion relations in pionpion and photonnucleon scattering In J Ballam et al eds High energy nuclear physics in Proceedings of the Sixth Annual Rochester Conference Rochester New York USA April 37 1956 pp 306 New York Interscience Publishers The dispersion relations were analytic properties of the SmatrixRickles 2014 p 29 and they imposed more stringent conditions than those that follow from unitarity alone This development in Smatrix theory stemmed from Murray GellMann and Marvin Leonard Goldbergers 1954 discovery of crossing symmetry another condition that the Smatrix had to fulfilGellMann M and Goldberger M L 1954 The scattering of low energy photons by particles of spin 12 Physical Review 96 14338 Prominent advocates of the new dispersion relations approach included Stanley Mandelstam and Geoffrey Chew both at UC Berkeley at the time Mandelstam discovered the double dispersion relations a new and powerful analytic form in 1958 and believed that it would provide the key to progress in the intractable strong interactions 雷格理論 1950 年代後期，不同人各自發現了存在許多自旋更高的強相互作用粒子，這很明顯非基本粒子。 By the late 1950s many strongly interacting particles of ever higher spins had been discovered and it became clear that they were not all fundamental While Japanese physicist Shoichi Sakata proposed that the particles could be understood as bound states of just three of them the proton the neutron and the Lambda see Sakata model Geoffrey Chew believed that none of these particles are fundamentalChew G 1962 SMatrix theory of strong interactions New York WA Benjamin p 32 for details see Bootstrap model Sakatas approach was reworked in the 1960s into the quark model by Murray GellMann and George Zweig by making the charges of the hypothetical constituents fractional and rejecting the idea that they were observed particles At the time Chews approach was considered more mainstream because it did not introduce fractional charge values and because it focused on experimentally measurable Smatrix elements not on hypothetical pointlike constituents In 1959 Tullio Regge a young theorist in Italy discovered that bound states in quantum mechanics can be organized into families known as Regge trajectories each family having distinctive angular momentaRegge Tullio Introduction to complex angular momentum Il Nuovo Cimento Series 10 Vol 14 1959 p 951 This idea was generalized to relativistic quantum mechanics by Stanley Mandelstam Vladimir Gribov and using a mathematical method the SommerfeldWatson representation discovered decades earlier by Arnold Sommerfeld and the result was dubbed the FroissartGribov formulaWhite Alan R 2000 The Past and Future of SMatrix Theory In 1961 Geoffrey Chew and Steven Frautschi recognized that mesons had straight line Regge trajectories in their scheme spin is plotted against mass squared on a socalled ChewFrautschi plot which implied that the scattering of these particles would have very strange behaviorit should fall off exponentially quickly at large angles With this realization theorists hoped to construct a theory of composite particles on Regge trajectories whose scattering amplitudes had the asymptotic form demanded by Regge theory In 1967 a notable step forward in the bootstrap approach was the principle of DHS duality introduced by Richard Dolen David Horn and Christoph Schmid in 1967 at Caltech the original term for it was average duality or finite energy sum rule FESR duality The three researchers noticed that Regge pole exchange at high energy and resonance at low energy descriptions offer multiple representationsapproximations of one and the same physically observable processRickles 2014 pp 389 雙共振模型 由加布裡埃萊韋內齊亞諾義大利弦論先驅於 1968 年建構。 The first model in which hadronic particles essentially follow the Regge trajectories was the dual resonance model that was constructed by Gabriele Veneziano in 1968 who noted that the Euler beta function could be used to describe 4particle scattering amplitude data for such particles The Veneziano scattering amplitude or Veneziano model was quickly generalized to an Nparticle amplitude by Ziro Koba and Holger Bech Nielsen their approach was dubbed the KobaNielsen formalism and to what are now recognized as closed strings by Miguel Virasoro and Joel A Shapiro their approach was dubbed the ShapiroVirasoro model In 1969 the ChanPaton rules proposed by Jack E Paton and HongMo Chan enabled isospin factors to be added to the Veneziano modelRickles 2014 p 5 In 196970 Yoichiro NambuNambu Y 1970 Quark model and the factorization of the Veneziano amplitude In R Chand ed Symmetries and Quark Models Proceedings of the International Conference held at Wayne State University Detroit Michigan June 1820 1969 pp 269277 Singapore World Scientific Holger Bech NielsenNielsen H B An almost physical interpretation of the dual N point function Nordita preprint 1969 unpublished and Leonard Susskind presented a physical interpretation of the Veneziano amplitude by representing nuclear forces as vibrating onedimensional strings However this stringbased description of the strong force made many predictions that directly contradicted experimental findings In 1971 Pierre Ramond and independently John H Schwarz and André Neveu attempted to implement fermions into the dual model This led to the concept of spinning strings and pointed the way to a method for removing the problematic tachyon see RNS formalismRickles 2014 p 97 Dual resonance models for strong interactions were a relatively popular subject of study between 1968 and 1973Rickles 2014 pp 56 44 The scientific community lost interest in string theory as a theory of strong interactions in 1973 when quantum chromodynamics became the main focus of theoretical researchRickles 2014 p 77 mainly due to the theoretical appeal of its asymptotic freedomRickles 2014 p 11 n 22 玻色弦理論和超弦理論 玻色弦理論 1974 年，約翰席瓦茲和若埃爾捨克、米穀民明先驅建構。 他們研究了玻色子弦振動，發現特性與引力子匹配。這導致了玻色子弦理論的發展。 弦理論是根據泊裡雅科夫作用量 Zwiebach Barton 2009 A First Course in String Theory Cambridge University Press p 582 描述弦如何在空間和時間中移動。像彈簧一樣，弦往往會收縮以最小化其勢能，但能量守恆會阻止它們消失而振盪。透過將量子力學應用於弦，可以推斷出弦不同振動模式，每個振動狀態又皆是不同粒子。每粒粒子的質量，以及相互作用的方式，都是由弦的振動方式決定。 in essence by the note the string sounds The scale of notes each corresponding to a different kind of particle is termed the spectrum of the theory Early models included both open strings which have two distinct endpoints and closed strings where the endpoints are joined to make a complete loop The two types of string behave in slightly different ways yielding two spectra Not all modern string theories use both types some incorporate only the closed variety The earliest string model has several problems it has a critical dimension D 26 a feature that was originally discovered by Claud Lovelace in 1971 the theory has a fundamental instability the presence of tachyonsSakata Fumihiko Wu Ke Zhao EnGuang eds Frontiers of Theoretical Physics A General View of Theoretical Physics at the Crossing of Centuries World Scientific 2001 p 121 see tachyon condensation additionally the spectrum of particles contains only bosons particles like the photon that obey particular rules of behavior While bosons are a critical ingredient of the Universe they are not its only constituents Investigating how a string theory may include fermions in its spectrum led to the invention of supersymmetry in the West Rickles 2014 p 104 in 1971J L Gervais and B Sakita worked on the twodimensional case in which they use the concept of supergauge taken from Ramond Neveu and Schwarzs work on dual models a mathematical transformation between bosons and fermions String theories that include fermionic vibrations are now known as superstring theories In 1977 the GSO projection named after Ferdinando Gliozzi Joël Scherk and David I Olive led to a family of tachyonfree unitary free string theories the first consistent superstring theories see below 第一次超弦革命 The first superstring revolution is a period of important discoveries that began in 1984Rickles 2014 p 147 Green and Schwarzs anomaly cancellation paper triggered a very large increase in the production of papers on the subject including a related pair of papers that between them had the potential to provide the foundation for a realistic unified theory of both particle physics and gravity It was realized that string theory was capable of describing all elementary particles as well as the interactions between them Hundreds of physicists started to work on string theory as the most promising idea to unify physical theoriesRickles 2014 p 157 The revolution was started by a discovery of anomaly cancellation in type I string theory via the GreenSchwarz mechanism named after Michael Green and John H Schwarz in 1984Johnson Clifford V Dbranes Cambridge University Press 2006 pp 16970 The groundbreaking discovery of the heterotic string was made by David Gross Jeffrey Harvey Emil Martinec and Ryan Rohm in 1985 It was also realized by Philip Candelas Gary Horowitz Andrew Strominger and Edward Witten in 1985 that to obtain N1 supersymmetry the six small extra dimensions the D 10 critical dimension of superstring theory had been originally discovered by John H Schwarz in 1972 need to be compactified on a CalabiYau manifold In string theory compactification is a generalization of KaluzaKlein theory which was first proposed in the 1920s Rickles 2014 p 89 n 44 By 1985 five separate superstring theories had been described type IGreen M B Schwarz J H 1982 Supersymmetrical string theories Physics Letters B 109 444448 this paper classified the consistent tendimensional superstring theories and gave them the names Type I Type IIA and Type IIB type II IIA and IIB and heterotic Discover magazine in the November 1986 issue vol 7 11 featured a cover story written by Gary Taubes Everythings Now Tied to Strings which explained string theory for a popular audience In 1987 and Paul Townsend showed that there are no superstrings in eleven dimensions the largest number of dimensions consistent with a single graviton in supergravity theoriesThis was demonstrated in Nahm Werner Supersymmetries and their representations Nuclear Physics B 135 no 1 1978 pp 149166 doi10101605503213 78 902183 but supermembranesE Bergshoeff E Sezgin P K Townsend Supermembranes and ElevenDimensional Supergravity Phys Lett B 189 75 1987 第二次超弦革命 1990 年代，受對偶性的啟發，愛德華維頓造了個 11 維的 M 理論，把 5 種版本的 10 維超弦理論與 11 維超重力論推演成 M 理論的 6 個形。這些發現帶動了第二次超弦革命有數百篇論文出現。 In the early 1990s Edward Witten and others found strong evidence that the different superstring theories were different limits of an 11dimensional theoryIt was Edward Witten who observed that the theory must be an 11dimensional one in that became known as MtheoryWhen Witten named it Mtheory he did not specify what the M stood for presumably because he did not feel he had the right to name a theory he had not been able to fully describe The M sometimes is said to stand for Mystery or Magic or Mother More serious suggestions include Matrix or Membrane Sheldon Glashow has noted that the M might be an upside down W standing for Witten Others have suggested that the M in Mtheory should stand for Missing Monstrous or even Murky According to Witten himself as quoted in the PBS documentary based on Brian Greenes The Elegant Universe the M in Mtheory stands for magic mystery or matrix according to taste for details see Introduction to Mtheory These discoveries sparked the second superstring revolution that took place approximately between 1994 and 1995Rickles 2014 p 208 n 2 The different versions of superstring theory were unified as long hoped by new equivalences These are known as Sduality Tduality Uduality mirror symmetry and conifold transitions The different theories of strings were also related to Mtheory In 1995 Joseph Polchinski discovered that the theory requires the inclusion of higherdimensional objects called Dbranes these are the sources of electric and magnetic RamondRamond fields that are required by string dualityRickles 2014 p 212 Dbranes added additional rich mathematical structure to the theory and opened possibilities for constructing realistic cosmological models in the theory for details see Brane cosmology In 199798 Juan Maldacena conjectured a relationship between type IIB string theory and N 4 supersymmetric YangMills theory a gauge theory This conjecture called the AdSCFT correspondence has generated a great deal of interest in high energy physicsRickles 2014 p 207 It is a realization of the holographic principle which has farreaching implications the AdSCFT correspondence has helped elucidate the mysteries of black holes suggested by Stephen Hawkings workRickles 2014 p 222 and is believed to provide a resolution of the black hole information paradox p 63 千禧年 In 2003 Michael R Douglass discovery of the string theory landscapeDouglas Michael R The statistics of string M theory vacua JHEP 0305 46 2003 which suggests that string theory has a large number of inequivalent false vacuaThe most commonly quoted number is of the order 10500 See Ashok S Douglas M Counting flux vacua JHEP 0401 060 2004 led to much discussion of what string theory might eventually be expected to predict and how cosmology can be incorporated into the theoryRickles 2014 pp 2305 and 236 n 63 A possible mechanism of string theory vacuum stabilization the KKLT mechanism was proposed in 2003 by Shamit Kachru Renata Kallosh Andrei Linde and Sandip Trivedi 參考 進一步閱讀 Category 量子場論 Category 弦理論