Please answer this: Extract the answer to the question from the following context. Question: The lowest energy state of a volume of space is mathematically know as what? Context: In quantum mechanics and quantum field theory, the vacuum is defined as the state (that is, the solution to the equations of the theory) with the lowest possible energy (the ground state of the Hilbert space). In quantum electrodynamics this vacuum is referred to as 'QED vacuum' to distinguish it from the vacuum of quantum chromodynamics, denoted as QCD vacuum. QED vacuum is a state with no matter particles (hence the name), and also no photons. As described above, this state is impossible to achieve experimentally. (Even if every matter particle could somehow be removed from a volume, it would be impossible to eliminate all the blackbody photons.) Nonetheless, it provides a good model for realizable vacuum, and agrees with a number of experimental observations as described next.
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Answer: the ground state of the Hilbert space

Please answer this: Extract the answer to the question from the following context. Question: What was occupied in the 1800s? Context: When Russia invaded the Turkish Balkans in 1853, fears of Russian dominance in the Mediterranean and Middle East led Britain and France to invade the Crimean Peninsula to destroy Russian naval capabilities. The ensuing Crimean War (185456), which involved new techniques of modern warfare, and was the only global war fought between Britain and another imperial power during the Pax Britannica, was a resounding defeat for Russia. The situation remained unresolved in Central Asia for two more decades, with Britain annexing Baluchistan in 1876 and Russia annexing Kirghizia, Kazakhstan, and Turkmenistan. For a while it appeared that another war would be inevitable, but the two countries reached an agreement on their respective spheres of influence in the region in 1878 and on all outstanding matters in 1907 with the signing of the Anglo-Russian Entente. The destruction of the Russian Navy by the Japanese at the Battle of Port Arthur during the Russo-Japanese War of 190405 also limited its threat to the British.
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Answer: capabilities

Please answer this: Extract the answer to the question from the following context. Question: Besides London, the Bank of England's home is not where? Context: London's largest industry is finance, and its financial exports make it a large contributor to the UK's balance of payments. Around 325,000 people were employed in financial services in London until mid-2007. London has over 480 overseas banks, more than any other city in the world. Over 85 percent (3.2 million) of the employed population of greater London works in the services industries. Because of its prominent global role, London's economy had been affected by the Late-2000s financial crisis. However, by 2010 the City has recovered; put in place new regulatory powers, proceeded to regain lost ground and re-established London's economic dominance. The City of London is home to the Bank of England, London Stock Exchange, and Lloyd's of London insurance market.
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Answer:
any other city