Remarks on local symmetry invariance in perturbative algebraic quantum field theory

TL;DR

This paper proves that the quantum BV operator can be expressed as a commutator with the interacting BRST charge in a broad class of gauge theories within perturbative algebraic quantum field theory, extending previous results.

Contribution

It generalizes the relation between the BV operator and BRST charge to a wider class of theories with local symmetries, including gravity and string theory.

Findings

Quantum BV operator equals the commutator with the interacting BRST charge.

Applicable to general relativity and bosonic string theories.

Provides insights into gauge invariance and quantization approaches.

Abstract

We investigate various aspects of invariance under local symmetries 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 and the bosonic string. 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.