Premium
Noether Charges for self‐interacting quantum field theories in curved spacetimes with a Killing‐vector
Author(s) -
Hollands Stefan
Publication year - 2001
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/1521-3889(200109)10:10<859::aid-andp859>3.0.co;2-9
Subject(s) - noether's theorem , physics , killing vector field , spacetime , mathematical physics , quantum field theory , charge (physics) , field (mathematics) , quantum , symmetry (geometry) , classical mechanics , quantum mechanics , theoretical physics , lagrangian , pure mathematics , mathematics , geometry
We consider a self‐interacting, perturbative Klein‐Gordon quantum field in a curved spacetime admitting 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, in a certain sense, as a surface integral over the time‐component of some 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.