# Quantum BRST charge in gauge theories in curved space-time

## TL;DR

This paper develops a quantum BRST framework for gauge theories in curved space-time, establishing identities that ensure gauge symmetry is preserved at the quantum level in a model-independent way.

## Contribution

It introduces a new quantum BRST differential and anti-bracket, extending classical gauge symmetry concepts to curved space-time within renormalized perturbation theory.

## Key findings

- Derived an identity relating the quantum BRST charge to a new differential and anti-bracket.
- Proved gauge symmetry preservation at the quantum level in a model-independent manner.
- Extended the algebraic structure of gauge observables to curved space-time.

## Abstract

Renormalized gauge-invariant observables in gauge theories form an algebra which is obtained as the cohomology of the derivation $[\textbf{Q}_L, -]$ with $\textbf{Q}_L$ the renormalized interacting quantum BRST charge. For a large class of gauge theories in Lorentzian globally hyperbolic space-times, we derive an identity in renormalized perturbation theory which expresses the commutator $[\textbf{Q}_L, -]$ in terms of a new nilpotent quantum BRST differential and a new quantum anti-bracket which differ from their classical counterparts by certain quantum corrections. This identity enables us to prove different manifestations of gauge symmetry preservation at the quantum level in a model-independent fashion.