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Keywords = Gribov–Zwanziger theory

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39 pages, 592 KiB  
Article
Non-Abelian Gauge Theories with Composite Fields in the Background Field Method
by Pavel Yur’evich Moshin, Alexander Alexandrovich Reshetnyak and Ricardo Alexander Castro
Universe 2023, 9(1), 18; https://doi.org/10.3390/universe9010018 - 27 Dec 2022
Cited by 1 | Viewed by 1638
Abstract
Non-Abelian gauge theories with composite fields are examined in the background field method. Generating functionals of Green’s functions for a Yang–Mills theory with composite and background fields are introduced, including the generating functional of vertex Green’s functions (effective action). The corresponding Ward identities [...] Read more.
Non-Abelian gauge theories with composite fields are examined in the background field method. Generating functionals of Green’s functions for a Yang–Mills theory with composite and background fields are introduced, including the generating functional of vertex Green’s functions (effective action). The corresponding Ward identities are obtained, and the issue of gauge dependence is investigated. A gauge variation of the effective action is found in terms of a nilpotent operator depending on the composite and background fields. On-shell independence from the choice of gauge fixing for the effective action is established. In the study of the Ward identities and gauge dependence, finite field-dependent BRST transformations with a background field are introduced and employed on a systematic basis. On the one hand, this involves the consideration of (modified) Ward identities with a field-dependent anticommuting parameter, also depending on a non-trivial background. On the other hand, the issue of gauge dependence is studied with reference to a finite variation of the gauge Fermion. The concept of a joint introduction of composite and background fields to non-Abelian gauge theories is exemplified by the Gribov–Zwanziger theory, including the case of a local BRST-invariant horizon, and also by the Volovich–Katanaev model of two-dimensional gravity with dynamical torsion. Full article
(This article belongs to the Section Field Theory)
26 pages, 465 KiB  
Article
Composite and Background Fields in Non-Abelian Gauge Models
by Pavel Yu. Moshin and Alexander A. Reshetnyak
Symmetry 2020, 12(12), 1985; https://doi.org/10.3390/sym12121985 - 30 Nov 2020
Cited by 1 | Viewed by 1847
Abstract
A joint introduction of composite and background fields into non-Abelian quantum gauge theories is suggested based on the symmetries of the generating functional of Green’s functions, with the systematic analysis focused on quantum Yang–Mills theories, including the properties of the generating functional of [...] Read more.
A joint introduction of composite and background fields into non-Abelian quantum gauge theories is suggested based on the symmetries of the generating functional of Green’s functions, with the systematic analysis focused on quantum Yang–Mills theories, including the properties of the generating functional of vertex Green’s functions (effective action). For the effective action in such theories, gauge dependence is found in terms of a nilpotent operator with composite and background fields, and on-shell independence from gauge fixing is established. The basic concept of a joint introduction of composite and background fields into non-Abelian gauge theories is extended to the Volovich–Katanaev model of two-dimensional gravity with dynamical torsion, as well as to the Gribov–Zwanziger theory. Full article
(This article belongs to the Special Issue Quantum Gravity Condensates)
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