Noether Charges for Self-interacting Quantum Field Theories in Curved Spacetimes with a Killing-vector
arXiv:gr-qc/0011069 · doi:10.1002/1521-3889(200109)10:10<859::AID-ANDP859>3.0.CO;2-9
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.
Latex, 29 pages, no figures. v2: minor corrections and rewordings, v3: typos corrected