# zbMATH — the first resource for mathematics

Quantum BRST charge in gauge theories in curved space-time. (English) Zbl 1406.81067
Summary: Renormalized gauge-invariant observables in gauge theories form an algebra which is obtained as the cohomology of the derivation $$\left[\mathbf{Q}_L, -\right],\; \text{with}\; \mathbf {Q}_{L}$$ 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 $$[\mathbf{Q}_{L}, -]$$ 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.{