• DOI:10.1063/1.2897049
• Corpus ID: 14640463

Equivariant symplectic geometry of gauge fixing in Yang–Mills theory

@article{Akant2007EquivariantSG,
  title={Equivariant symplectic geometry of gauge fixing in Yang–Mills theory},
  author={Levent Akant},
  journal={Journal of Mathematical Physics},
  year={2007},
  volume={49},
  pages={033512}
}

• L. Akant
• Published 13 March 2007
• Mathematics, Physics
• Journal of Mathematical Physics

The Faddeev–Popov gauge fixing in Yang–Mills theory is interpreted as equivariant localization. It is shown that the Faddeev–Popov 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 4-form, 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...