Advertisement

Communications in Mathematical Physics

, Volume 219, Issue 1, pp 5–30 | Cite as

Algebraic Quantum Field Theory, Perturbation Theory, and the Loop Expansion

  • M. Dütsch
  • K. Fredenhagen

Abstract:

The perturbative treatment of quantum field theory is formulated within the framework of algebraic quantum field theory. We show that the algebra of interacting fields is additive, i.e. fully determined by its subalgebras associated to arbitrary small subregions of Minkowski space. We also give an algebraic formulation of the loop expansion by introducing a projective system ?( n ) of observables “up to n loops”, where ?(0) is the Poisson algebra of the classical field theory. Finally we give a local algebraic formulation for two cases of the quantum action principle and compare it with the usual formulation in terms of Green's functions.

Keywords

Field Theory Quantum Field Theory Perturbation Theory Minkowski Space Action Principle 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • M. Dütsch
    • 1
  • K. Fredenhagen
    • 1
  1. 1.II. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, Hamburg, Germany.¶E-mail: duetsch@mail.desy.de, fredenha@x4u2.desy.deDE

Personalised recommendations