Equivariant BRST quantization and reducible symmetries

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.