Cohomological analysis of gauge-fixed gauge theories

The relation between the gauge-invariant local BRST cohomology involving the antifields and the gauge-fixed BRST cohomology is clarified. It is shown in particular that the cocycle conditions become equivalent once it is imposed, on the gauge-fixed side, that the BRST cocycles should yield deformations that preserve the nilpotency of the (gauge-fixed) BRST differential. This shows that the restrictions imposed on local counterterms by the quantum Noether condition in the Epstein–Glaser construction of gauge theories are equivalent to the restrictions imposed by BRST invariance on local counterterms in the standard Lagrangian approach.