Anomalies in time-ordered products and applications to the BV-BRST formulation of quantum gauge theories

Abstract

We show that every (graded) derivation on the algebra of free quantum fields and their Wick powers in curved spacetimes gives rise to a set of anomalous Ward identities for time-ordered products, with an explicit formula for their classical limit. We study these identities for the Koszul-Tate and the full BRST differential in the BV-BRST formulation of perturbatively interacting quantum gauge theories, and clarify the relation to previous results. In particular, we show that the quantum BRST differential, the quantum antibracket and the higher-order anomalies form an $L_{\infty }$ algebra. The defining relations of this algebra ensure that the gauge structure is well-defined on cohomology classes of the quantum BRST operator, i.e., observables. Furthermore, we show that one can determine contact terms such that also the interacting time-ordered products of multiple interacting fields are well defined on cohomology classes. An important technical improvement over previous treatments is the fact that all our relations hold off-shell and are independent of the concrete form of the Lagrangian, including the case of open gauge algebras.

64 pages, minor corrections and additions throughout, matches published version

References in corpus (6)

• The Unruh effect and its applications
• Removal of violations of the Master Ward Identity in perturbative QFT
• Gauge-invariant quantum gravitational corrections to correlation functions
• Propagators for gauge-invariant observables in cosmology
• Weak adiabatic limit in quantum field theories with massless particles
• On Wick polynomials of boson fields in locally covariant algebraic QFT

Cited by in corpus (6)

• Trace anomaly for Weyl fermions using the Breitenlohner-Maison scheme for ${\gamma }_{\ast }$
• Background independence in gauge theories
• A Lorentzian renormalisation group equation for gauge theories
• The Sine-Gordon QFT in de Sitter spacetime
• Background independence and the Adler-Bardeen theorem
• The Weyl anomaly in interacting quantum field theory on curved spacetimes