Non-Abelian Gauge Theories with Composite Fields in the Background Field Method
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). T...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-12-01
|
| Series: | Universe |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2218-1997/9/1/18 |
| _version_ | 1797436596253884416 |
|---|---|
| author | Pavel Yur’evich Moshin Alexander Alexandrovich Reshetnyak Ricardo Alexander Castro |
| author_facet | Pavel Yur’evich Moshin Alexander Alexandrovich Reshetnyak Ricardo Alexander Castro |
| author_sort | Pavel Yur’evich Moshin |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T11:04:55Z |
| format | Article |
| id | doaj.art-31fc286f554440a7b4fea382fd2ef1b9 |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-03-09T11:04:55Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-31fc286f554440a7b4fea382fd2ef1b92023-12-01T00:58:58ZengMDPI AGUniverse2218-19972022-12-01911810.3390/universe9010018Non-Abelian Gauge Theories with Composite Fields in the Background Field MethodPavel Yur’evich Moshin0Alexander Alexandrovich Reshetnyak1Ricardo Alexander Castro2Laboratory for Quantum Theory of Intense Fields, Faculty of Physics, National Research Tomsk State University, 634050 Tomsk, RussiaLaboratory for Quantum Theory of Intense Fields, Faculty of Physics, National Research Tomsk State University, 634050 Tomsk, RussiaDepartment of Nuclear Physics, Institute of Physics, University of São Paulo, São Paulo CEP 05508-090, BrazilNon-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.https://www.mdpi.com/2218-1997/9/1/18non-Abelian gauge theoriescomposite fieldsbackground field methodeffective actionfield-dependent BRST transformationsWard identities |
| spellingShingle | Pavel Yur’evich Moshin Alexander Alexandrovich Reshetnyak Ricardo Alexander Castro Non-Abelian Gauge Theories with Composite Fields in the Background Field Method Universe non-Abelian gauge theories composite fields background field method effective action field-dependent BRST transformations Ward identities |
| title | Non-Abelian Gauge Theories with Composite Fields in the Background Field Method |
| title_full | Non-Abelian Gauge Theories with Composite Fields in the Background Field Method |
| title_fullStr | Non-Abelian Gauge Theories with Composite Fields in the Background Field Method |
| title_full_unstemmed | Non-Abelian Gauge Theories with Composite Fields in the Background Field Method |
| title_short | Non-Abelian Gauge Theories with Composite Fields in the Background Field Method |
| title_sort | non abelian gauge theories with composite fields in the background field method |
| topic | non-Abelian gauge theories composite fields background field method effective action field-dependent BRST transformations Ward identities |
| url | https://www.mdpi.com/2218-1997/9/1/18 |
| work_keys_str_mv | AT pavelyurevichmoshin nonabeliangaugetheorieswithcompositefieldsinthebackgroundfieldmethod AT alexanderalexandrovichreshetnyak nonabeliangaugetheorieswithcompositefieldsinthebackgroundfieldmethod AT ricardoalexandercastro nonabeliangaugetheorieswithcompositefieldsinthebackgroundfieldmethod |