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

March 12, 2017

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. This quotient
algebra then admits a Hilbert space representation. 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 differential $\hat{q}$, the
quantum BRST differential, which differs from the classical one 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.

Keywords:

*none*