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367:{\displaystyle A_{\mu }^{a}(x)={\bar {\eta }}_{\mu \nu }^{a}\Pi (x)\partial _{\nu }\Pi ^{-1}(x)\quad {\text{with}}\quad \Pi (x)=1+{\frac {\pi \rho ^{2}T}{r}}{\frac {\sinh(2\pi rT)}{\cosh(2\pi rT)-\cos(2\pi \tau T)}}\ ,}
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Philipp
Gerhold; Ernst-Michael Ilgenfritz; Michael MĂźller-Preussker (2007). "Improved superposition schemes for approximate multi-caloron configurations".
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98:, at finite temperature, the Euclidean time dimension is periodic, which means that instanton solutions have to be periodic as well.
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94:). This changes the overall structure of spacetime, and thus also changes the form of the instanton solutions. According to the
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Finite temperatures in quantum field theories are modeled by compactifying the imaginary (Euclidean) time (see
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Harrington, Barry; Shepard (1978). "Periodic
Euclidean Solutions and the Finite Temperature YangâMills Gas".
43:
of the
Euclidean version of the theory under consideration, and which are furthermore localized in Euclidean
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Shnir (2006). "Self-dual and non-self dual axially symmetric caloron solutions in SU(2) Yang-Mills theory".
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is the temperature. This solution was found based on a periodic multi-instanton solution first suggested by
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Dmitri
Diakonov; Nikolay Gromov (2005). "SU(N) caloron measure and its relation to instantons".
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At zero temperature, instantons are the name given to solutions of the classical
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603:(1977). "Some Exact Multi-Instanton Solutions of Classical YangâMills Theory".
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of the
Minkowski theory. One important example of an instanton is the
501:(1975). "Pseudoparticle solutions of the YangâMills equations".
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Daniel
Nogradi (2005). "Multi-calorons and their moduli".
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at zero temperature, the instantons have the form of the
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83:field equations in Euclidean spacetime (i.e. after
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92:thermal quantum field theory
16:Finite temperature instanton
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724:10.1103/PhysRevD.72.025003
669:Instantons in Gauge Theory
627:10.1103/PhysRevLett.38.121
457:is the Euclidean time and
102:In SU(2) YangâMills theory
575:10.1103/PhysRevD.17.2122
59:, discovered in 1975 by
606:Physical Review Letters
837:-related article is a
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893:Quantum physics stubs
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450:{\displaystyle \tau }
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473:References and notes
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21:mathematical physics
795:2007NuPhB.774..268G
716:2005PhRvD..72b5003D
644:Das, Ashok (1997).
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567:1978PhRvD..17.2122H
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81:YangâMills
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230:Π
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179:Π
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166:μ
159:¯
156:η
130:μ
106:In SU(2)
49:tunneling
45:spacetime
29:instanton
491:Polyakov
463:'t Hooft
69:Schwartz
65:Polyakov
791:Bibcode
712:Bibcode
615:Bibcode
563:Bibcode
513:Bibcode
499:Tyupkin
73:Tyupkin
61:Belavin
25:caloron
809:
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467:Witten
377:where
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833:This
807:S2CID
781:arXiv
756:arXiv
741:arXiv
728:S2CID
702:arXiv
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839:stub
677:ISBN
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537:See
305:cosh
279:sinh
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71:and
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