Renormalization and quantum field theory. (English) Zbl 1243.22021

Borcherds, Richard E.

Algebra Number Theory 5, No. 5, 627-658 (2011).

Summary: 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.

MSC:

22E70

Applications of Lie groups to the sciences; explicit representations

Keywords:

quantum field theory; renormalization; Feynman measure; Hopf algebra; Feynman diagram