Quantum BRST charge in gauge theories in 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2017
- DOI:
- 10.48550/arXiv.1703.04148
- arXiv:
- arXiv:1703.04148
- Bibcode:
- 2017arXiv170304148T
- Keywords:
-
- High Energy Physics - Theory;
- General Relativity and Quantum Cosmology;
- Mathematical Physics
- E-Print:
- 41 pages, 1 figure, v3: Intoduction rewritten, Proposition 14 replaced by Lemma 14, Theorem 16 omitted, Theorem 18 replaced by Theorem 16 and its proof corrected, lemma 11 replaced by Theorem 19, comparison with RG flow equation added, Results unchanged