Renormalization and quantum field theory

TL;DR

This paper explains how to use regularization and renormalization techniques to build a consistent perturbative quantum field theory from a Lagrangian, extending axioms to curved spacetimes.

Contribution

It introduces a canonical orbit of Feynman measures under renormalization and constructs a perturbative QFT satisfying extended Wightman axioms.

Findings

Existence of a canonical orbit of Feynman measures

Construction of perturbative QFT from a Lagrangian and Feynman measure

Extension of Wightman axioms to curved spacetimes

Abstract

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.