Cohomological analysis of gauged-fixed gauge theories
Glenn Barnich, Marc Henneaux, Tobias Hurth, Kostas Skenderis
TL;DR
This paper clarifies the relationship between gauge-invariant and gauge-fixed BRST cohomology, showing their equivalence under certain conditions, and relates restrictions on local counterterms in different formulations of gauge theories.
Contribution
It demonstrates the equivalence of gauge-invariant and gauge-fixed BRST cohomology cocycle conditions and connects restrictions on local counterterms across different quantization approaches.
Findings
Gauge-invariant and gauge-fixed BRST cohomologies are equivalent under certain conditions.
Restrictions on local counterterms are consistent across different gauge theory formulations.
The results unify the understanding of BRST cohomology in gauge theories.
Abstract
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.
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