Gauge fixing and abelianization in simple BRST quantization

In a previous paper [Nucl. Phys. B395 (1993) 647]it was shown that the BRST charge Q for any gauge model with a Lie algebra symmetry may be decomposed as Q=δ+δ†, δ2=δ†2=0, [δ,δ†]+ = 0 provided dynamical Lagrange multipliers are used, but without introducing other matter variables in δ than the gauge generators in Q. In this paper further decompositions are derived, but now by means of gauge fixing operators. As in the previous paper it is shown that δ=c†aφa, where ca are new ghosts and φa are non-hermitian variables satisfying the gauge algebra. However, in distinction to the previous paper also solutions of the form δ=c†aAa, where the Aa satisfy an abelian algebra, are derived (abelianization). By means of a bigrading the BRST condition reduces to δvertical stroke ph right angle =δ†vertical stroke ph right angle =0 on inner product spaces whose general solutions are expressed in terms of the solutions to a proper Dirac quantization. Thus, the procedure provides for inner products for the solutions of a Dirac quantization. (orig.)