Abstract:
We present a perturbative construction of interacting quantum field theories on smooth globally hyperbolic (curved) space-times. We develop a purely local version of the Stückelberg–Bogoliubov–Epstein–Glaser method of renormalization by using techniques from microlocal analysis. Relying on recent results of Radzikowski, Köhler and the authors about a formulation of a local spectrum condition in terms of wave front sets of correlation functions of quantum fields on curved space-times, we construct time-ordered operator-valued products of Wick polynomials of free fields. They serve as building blocks for a local (perturbative) definition of interacting fields. Renormalization in this framework amounts to extensions of expectation values of time-ordered products to all points of space-time. The extensions are classified according to a microlocal generalization of Steinmann scaling degree corresponding to the degree of divergence in other renormalization schemes.
As a result, we prove that the usual perturbative classification of interacting quantum field theories holds also on curved space-times. Finite renormalizations are deferred to a subsequent paper.
As byproducts, we describe a perturbative construction of local algebras of observables, present a new definition of Wick polynomials as operator-valued distributions on a natural domain, and we find a general method for the extension of distributions which were defined on the complement of some surface.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 31 March 1999 / Accepted: 10 June 1999
Rights and permissions
About this article
Cite this article
Brunetti, R., Fredenhagen, K. Microlocal Analysis and¶Interacting Quantum Field Theories:¶Renormalization on Physical Backgrounds. Comm Math Phys 208, 623–661 (2000). https://doi.org/10.1007/s002200050004
Issue Date:
DOI: https://doi.org/10.1007/s002200050004