Solving general gauge theories on inner product spaces Original Research Article

By means of a generalized quartet mechanism we show in a model independent way that a BRST quantization on an inner product space leads to physical states of the form ph〉 = exp [Q, ψ]ph〉0 where Q is the nilpotent BRST operator, ψ a hermitian fermionic gauge-fixing operator, and ph〉o BRST invariant states determined by a hermitian set of BRST doublets in involution. ph〉0 does not belong to an inner product space although ph〉 does. Since the BRST quartets are split into two sets of hermitian BRST doublets there are two choices for ph〉0 and the corresponding ψ. When applied to general, both irreducible and reducible, gauge theories of arbitrary rank within the BFV formulation we find that ph〉0 are trivial BRST invariant states which only depend on the matter variables for one set of solutions, and for the other set ph〉0 are solutions of a Dirac quantization. This generalizes previous Lie group solutions obtained by means of a bigrading.