Remarks on local gauge invariance in perturbative algebraic quantum field theory

Kasia Rejzner
January 29, 2013
In the present paper we investigate various aspects of local gauge invariance in the framework of perturbative algebraic quantum field theory (pAQFT). Our main result is the proof that the quantum Batalin-Vilkovisky (BV) operator, on-shell, can be written as the commutator with the interacting BRST charge. Up to now this was proven only for a certain class of fields in quantum electrodynamics and in Yang-Mills theory. Our result is more general and it holds in a wide class of theories with local symmetries, including general relativity. We also comment on other issues related to local gauge invariance and, using the language of homological algebra, we compare different approaches to quantization of gauge theories in the pAQFT framework.