Gauge fixing and coBRST

Abstract

It has previously been shown that a BRST quantization on an inner product space leads to physical states of the form |ph>=e^[Q, ψ] |ϕ> where |ϕ> is either a trivially BRST invariant state which only depends on the matter variables, |ϕ>_1, or a solution of a Dirac quantization, |ϕ>_2. ψis a corresponding fermionic gauge fixing operator, ψ_1 or ψ_2. We show here for abelian and nonabelian models that one may also choose a linear combination of ψ_1 and ψ_2 for both choices of |ϕ> except for a discrete set of relations between the coefficients. A general form of the coBRST charge operator is also determined and shown to be equal to such a ψfor an allowed linear combination of ψ_1 and ψ_2. This means that the coBRST charge is always a good gauge fixing fermion.