(Anti-)self-dual homogeneous vacuum gluon field as an origin of confinement and SUL(NF) × SUR(NF) symmetry breaking in QCD

It is shown that an (anti-) self-dual homogeneous vacuum gluon field appears in a natural way within the problem of calculation of the QCD partition function in the form of Euclidean functional integral with periodic boundary conditions. There is no violation of cluster property within this formulat...

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Bibliographic Details
Published in:The European physical journal. C, Particles and fields Particles and fields, 1998-03, Vol.1 (1-2), p.343-350
Main Authors: Efimov, G. V., Nedelko, S. N.
Format: Article
Language:English
Subjects:
Boundary conditions
Broken symmetry
Condensates
Confinement
Gluons
Mathematical analysis
Order parameters
Partitions (mathematics)
Quantum chromodynamics
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Summary:It is shown that an (anti-) self-dual homogeneous vacuum gluon field appears in a natural way within the problem of calculation of the QCD partition function in the form of Euclidean functional integral with periodic boundary conditions. There is no violation of cluster property within this formulation, nor are parity, color and rotational symmetries broken explicitly. The massless limit of the product of the quark masses and condensates,% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWexLMBb50ujb% qeguuDJXwAKbacfiGae8xBa02aaSbaaKqaahaacWaGq9Nzaygaleqa% aOWaaaWaaeaaruauHXwy0LMBVbctP52B0LhCLbacgiGab4hYdyaara% WaaSbaaKqaahaacWaGq9NzaygaleqaaOGaa4hYdmaaBaaajeaWbaGa% maiu-zgaMbWcbeaaaOGaayzkJiaawQYiaaaa!50FF!, is calculated to all loop orders. This quantity does not vanish and is proportional to the gluon condensate appearing due to the nonzero strength of the vacuum gluon field. We conclude that the gluon condensate can be considered as an order parameter both for confinement and chiral symmetry breaking.
ISSN:1434-6044
1434-6052
DOI:10.1007/BF01245823