Renormalization and quantum field theory

Physics – Mathematical Physics

Scientific paper

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30 pages Revised version fixes a gap in the definition of Feynman measure, and has other minor changes

Scientific paper

10.2140/ant.2011.5.627

The aim of this paper is to describe how to use regularization and renormalization to construct a perturbative quantum field theory from a Lagrangian. We first define renormalizations and Feynman measures, and show that although there need not exist a canonical Feynman measure, there is a canonical orbit of Feynman measures under renormalization. We then construct a perturbative quantum field theory from a Lagrangian and a Feynman measure, and show that it satisfies perturbative analogues of the Wightman axioms, extended to allow time-ordered composite operators over curved spacetimes.

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