Equivariant BRST quantization and reducible symmetries

TL;DR

This paper develops a method for quantizing Hamiltonian systems with reducible symmetries using equivariant BRST cohomology, connecting it with BV quantization and equivariant de Rham theory.

Contribution

It introduces an equivariant BRST quantization approach for systems with reducible symmetry, linking it to BV formalism and equivariant cohomology.

Findings

Constructed a reduced phase space for systems with reducible symmetry.

Established the equivalence between BRST and BV quantization methods.

Applied the framework to a topological model related to equivariant cohomology.

Abstract

Working from first principles, quantization of a class of Hamiltonian systems with reducible symmetry is carried out by constructing first the appropriate reduced phase space and then the BRST cohomology. The constraints of this system correspond to a first class set for a group G and a second class set for a subgroup H. The BRST operator constructed is equivariant with respect to H. Using algebraic techniques analogous to those of equivariant de Rham theory, the BRST operator is shown to correspond to that obtained by BV quantization of a class of systems with reducible symmetry. The 'ghosts for ghosts' correspond to the even degree two generators in the Cartan model of equivariant cohomology. As an example of the methods developed, a topological model is described whose BRST quantization relates to the equivariant cohomology of a manifold under a circle action.