Microlocal Analysis andInteracting Quantum Field Theories:Renormalization on Physical Backgrounds
Abstract
We present a perturbative construction of interacting quantum field theories on any smooth globally hyperbolic manifold. We develop a purely local version of the StueckelbergBogoliubovEpsteinGlaser method of renormalization using techniques from microlocal analysis. As byproducts, we describe a perturbative construction of local algebras of observables, present a new definition of Wick polynomials as operatorvalued distributions on a natural domain, and we find a general method for the extension of distributions which were defined on the complement of some surfaces.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 2000
 DOI:
 10.1007/s002200050004
 arXiv:
 arXiv:mathph/9903028
 Bibcode:
 2000CMaPh.208..623B
 Keywords:

 Mathematical Physics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 81T05 (primary);
 81T20 (secondary)
 EPrint:
 38 pages, LaTeX with AMSLaTeX style option, Micro.tex macrofile