Physics – Mathematical Physics
Scientific paper
2010-07-31
Algebra & Number Theory 5-5 (2011), 627-658
Physics
Mathematical Physics
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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