Open Access
2011 Renormalization and quantum field theory
Richard Borcherds
Algebra Number Theory 5(5): 627-658 (2011). DOI: 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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Richard Borcherds. "Renormalization and quantum field theory." Algebra Number Theory 5 (5) 627 - 658, 2011.


Received: 23 August 2010; Revised: 18 February 2011; Accepted: 24 April 2011; Published: 2011
First available in Project Euclid: 20 December 2017

zbMATH: 1243.22021
MathSciNet: MR2889750
Digital Object Identifier: 10.2140/ant.2011.5.627

Primary: 22E70

Keywords: Feynman diagram , Feynman measure , Hopf algebra , Quantum field theory , renormalization

Rights: Copyright © 2011 Mathematical Sciences Publishers

Vol.5 • No. 5 • 2011
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