# 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} }

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…

## References

SHOWING 1-10 OF 91 REFERENCES

### Quantization of Gauge Systems

- Physics
- 1992

This is a systematic study of the classical and quantum theories of gauge systems. It starts with Dirac's analysis showing that gauge theories are constrained Hamiltonian systems. The classical…

### On the variation in the cohomology of the symplectic form of the reduced phase space

- Mathematics
- 1982

is called the momentum mapping of the Hamiltonian T-action. Given (1.1), the condition (1.2) just means that T acts along the fibers of J. For the basic definitions and properties of non-commutative…

### Non-Abelian localization for Chern-Simons theory

- Mathematics
- 2005

We reconsider Chern-Simons gauge theory on a Seifert manifold M (the total space of a nontrivial circle bundle over a Riemann surface). When M is a Seifert manifold, Lawrence and Rozansky have shown…

### BRST model for equivariant cohomology and representatives for the equivariant thom class

- Mathematics
- 1993

In this paper the BRST formalism for topological field theories is studied in a mathematical setting. The BRST operator is obtained as a member of a one parameter family of operators connecting the…

### Renormalization of the abelian Higgs-Kibble model

- Physics
- 1975

This article is devoted to the perturbative renormalization of the abelian Higgs-Kibble model, within the class of renormalizable gauges which are odd under charge conjugation. The Bogoliubov…

### Some remarks on BRS transformations, anomalies and the cohomology of the Lie algebra of the group of gauge transformations

- Mathematics
- 1983

We show that ghosts in gauge theories can be interpreted as Maurer-Cartan forms in the infinite dimensional group ℊ of gauge transformations. We examine the cohomology of the Lie algebra of ℊ and…