Noether Charges for Self-interacting Quantum Field Theories in Curved Spacetimes with a Killing-vector

TL;DR

This paper demonstrates that in self-interacting quantum field theories on curved spacetimes with a Killing vector, the spacetime symmetry can be represented by a Noether charge derived as a surface integral, supported by Ward identities.

Contribution

It establishes a method to implement spacetime symmetries via Noether charges in interacting QFTs on curved backgrounds, extending previous constructions.

Findings

Noether charge acts as symmetry generator for interacting fields.

Surface integral representation of the Noether charge is valid in curved spacetimes.

Ward identities underpin the symmetry implementation.

Abstract

We consider self-interacting, perturbative quantum field theory in a curved spacetime background with a Killing vector field. We show that the action of this spacetime symmetry on interacting field operators can be implemented by a Noether charge which arises as a surface integral over the time-component of the interacting Noether current-density associated with the Killing field. The proof of this involves the demonstration of a corresponding set of Ward identities. Our work is based on the perturbative construction by Brunetti and Fredenhagen (Commun.Math.Phys. 208 (2000) 623-661) of self-interacting quantum field theories in general globally hyperbolic spacetimes.