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

Mojtaba Taslimi Tehrani
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.