Quantum BRST charge in gauge theories in curved space-time

Renormalized gauge-invariant observables in gauge theories form an algebra which is obtained as the cohomology of the derivation QL,−, with QL as 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 [QL, −] in terms of a new nilpotent quantum BRST (Becchi, Rouet, Stora, Tyutin) 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.