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Communications in Mathematical Physics

, Volume 208, Issue 3, pp 623–661 | Cite as

Microlocal Analysis and¶Interacting Quantum Field Theories:¶Renormalization on Physical Backgrounds

  • Romeo Brunetti
  • Klaus Fredenhagen

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.

Keywords

Correlation Function Local Version Subsequent Paper Free Field Spectrum Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Romeo Brunetti
    • 1
  • Klaus Fredenhagen
    • 1
  1. 1.Institut für Theoretische Physik, Universität Hamburg,149 Luruper Chaussee, 22761 Hamburg, Germany. E-mail: brunetti@x4u2.desy.de; fredenha@x4u2.desy.deDE

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