# Anomalies in Time-Ordered Products and Applications to the BV–BRST Formulation of Quantum Gauge Theories

@article{Frb2019AnomaliesIT, title={Anomalies in Time-Ordered Products and Applications to the BV–BRST Formulation of Quantum Gauge Theories}, author={Markus B. Fr{\"o}b}, journal={Communications in Mathematical Physics}, year={2019} }

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…

## 4 Citations

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

- PhysicsJournal of Mathematical Physics
- 2019

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…

### Background Independence in Gauge Theories

- PhysicsAnnales Henri Poincaré
- 2020

Classical field theory is insensitive to the split of the field into a background configuration and a dynamical perturbation. In gauge theories, the situation is complicated by the fact that a…

### Trace anomaly for Weyl fermions using the Breitenlohner-Maison scheme for γ*

- PhysicsJournal of High Energy Physics
- 2021

We revisit the computation of the trace anomaly for Weyl fermions using dimensional regularization. For a consistent treatment of the chiral gamma matrix γ * in dimensional regularization, we work in…

### Background independence and the Adler-Bardeen theorem

- Physics
- 2022

We prove that for renormalizable Yang-Mills gauge theory with arbitrary compact gauge group (of at most a single abelian factor) and matter coupling, the absence of gauge anomalies can be established…

## References

SHOWING 1-10 OF 109 REFERENCES

### Renormalized Quantum Yang-Mills Fields in Curved Spacetime

- Mathematics, Physics
- 2008

We present a proof that the quantum Yang–Mills theory can be consistently defined as a renormalized, perturbative quantum field theory on an arbitrary globally hyperbolic curved, Lorentzian…

### Superconformal quantum field theory in curved spacetime

- Mathematics, Physics
- 2013

By conformally coupling vector and hyper multiplets in Minkowski space, we obtain a class of field theories with extended rigid conformal supersymmetry on any Lorentzian 4-manifold admitting twistor…

### Local BRST cohomology in gauge theories

- Mathematics, PhysicsPhysics Reports
- 2000

### Conservation of the Stress Tensor in Perturbative Interacting Quantum Field Theory in Curved Spacetimes

- Physics
- 2004

We propose additional conditions (beyond those considered in our previous papers) that should be imposed on Wick products and time-ordered products of a free quantum scalar field in curved spacetime.…

### Local Wick Polynomials and Time Ordered Products¶of Quantum Fields in Curved Spacetime

- Mathematics
- 2001

Abstract: In order to have well defined rules for the perturbative calculation of quantities of interest in an interacting quantum field theory in curved spacetime, it is necessary to construct Wick…

### Conservation of the stress tensor in interacting quantum field theory in curved spacetimes

- Physics
- 2004

We propose additional conditions (beyond those considered in our previous papers) that should be imposed on Wick products and time-ordered products of a free quantum scalar field in curved spacetime.…

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

- PhysicsJournal of Mathematical Physics
- 2019

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…

### Perturbative Algebraic Quantum Field Theory and the Renormalization Groups

- Physics
- 2009

A new formalism for the perturbative construction of algebraic quantum field theory is developed. The formalism allows the treatment of low dimensional theories and of non-polynomial interactions. We…

### Quantization of Gauge Systems

- Physics
- 1992

This is a systematic study of the classical and quantum theories of gauge systems. It starts with Dirac's analysis showing that gauge theories are constrained Hamiltonian systems. The classical…

### On the Renormalization Group in Curved Spacetime

- Physics, Mathematics
- 2003

Abstract: We define the renormalization group flow for a renormalizable interacting quantum field in curved spacetime via its behavior under scaling of the spacetime metric, g→λ2g. We consider…