Equivariant symplectic geometry of gauge fixing in YangMills theory
Abstract
The FaddeevPopov gauge fixing in YangMills theory is interpreted as equivariant localization. It is shown that the FaddeevPopov procedure amounts to a construction of a symplectic manifold with a Hamiltonian group action. The BRST cohomology is shown to be equivalent to the equivariant cohomology based on this symplectic manifold with Hamiltonian group action. The ghost operator is interpreted as a (pre)symplectic form and the gauge condition as the moment map corresponding to the Hamiltonian group action. This results in the identification of the gauge fixing action as a closed equivariant form, the sum of an equivariant symplectic form, and a certain closed equivariant 4form, which ensures convergence. An almost complex structure compatible with the symplectic form is constructed. The equivariant localization principle is used to localize the path integrals onto the gauge slice. The Gribov problem is also discussed in the context of equivariant localization principle. As a simple illustration of the methods developed in the paper, the partition function of N=2 supersymmetric quantum mechanics is calculated by equivariant localization.
 Authors:

 Feza Gursey Institute, Emek Mahallesi, Rasathane Yolu No. 68, Cengelkoy, Istanbul 346 84 (Turkey)
 Publication Date:
 OSTI Identifier:
 21100244
 Resource Type:
 Journal Article
 Journal Name:
 Journal of Mathematical Physics
 Additional Journal Information:
 Journal Volume: 49; Journal Issue: 3; Other Information: DOI: 10.1063/1.2897049; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 00222488
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CONVERGENCE; GEOMETRY; HAMILTONIANS; MAPS; PARTITION FUNCTIONS; PATH INTEGRALS; QUANTUM MECHANICS; SUPERSYMMETRY; YANGMILLS THEORY
Citation Formats
Akant, Levent. Equivariant symplectic geometry of gauge fixing in YangMills theory. United States: N. p., 2008.
Web. doi:10.1063/1.2897049.
Akant, Levent. Equivariant symplectic geometry of gauge fixing in YangMills theory. United States. https://doi.org/10.1063/1.2897049
Akant, Levent. Sat .
"Equivariant symplectic geometry of gauge fixing in YangMills theory". United States. https://doi.org/10.1063/1.2897049.
@article{osti_21100244,
title = {Equivariant symplectic geometry of gauge fixing in YangMills theory},
author = {Akant, Levent},
abstractNote = {The FaddeevPopov gauge fixing in YangMills theory is interpreted as equivariant localization. It is shown that the FaddeevPopov procedure amounts to a construction of a symplectic manifold with a Hamiltonian group action. The BRST cohomology is shown to be equivalent to the equivariant cohomology based on this symplectic manifold with Hamiltonian group action. The ghost operator is interpreted as a (pre)symplectic form and the gauge condition as the moment map corresponding to the Hamiltonian group action. This results in the identification of the gauge fixing action as a closed equivariant form, the sum of an equivariant symplectic form, and a certain closed equivariant 4form, which ensures convergence. An almost complex structure compatible with the symplectic form is constructed. The equivariant localization principle is used to localize the path integrals onto the gauge slice. The Gribov problem is also discussed in the context of equivariant localization principle. As a simple illustration of the methods developed in the paper, the partition function of N=2 supersymmetric quantum mechanics is calculated by equivariant localization.},
doi = {10.1063/1.2897049},
url = {https://www.osti.gov/biblio/21100244},
journal = {Journal of Mathematical Physics},
issn = {00222488},
number = 3,
volume = 49,
place = {United States},
year = {2008},
month = {3}
}