BASICS OF BRST QUANTIZATION ON INNER PRODUCT SPACES

Abstract

There is an elaborated abstract form of BRST quantization on inner product spaces within the operator formalism which leads to BRST-invariant states of the form [Formula: see text] where ψ is a gauge fixing fermion, and where |ϕ> is a BRST-invariant state determined by simple Hermitian conditions. These state representations are closely related to the path integral formulation. Here we analyse the basics of this approach in detail. The freedom in the choice of ψ and |ϕ> as well as their properties under gauge transformations are explicitly determined for simple Abelian models. In all considered cases SL(2,R) is shown both to be a natural extended gauge symmetry and to be useful to determine |ph>. The results are also applied to non-Abelian models.