Algebra & Number Theory

Renormalization and quantum field theory

Richard Borcherds

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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.

Article information

Algebra Number Theory, Volume 5, Number 5 (2011), 627-658.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 22E70: Applications of Lie groups to physics; explicit representations [See also 81R05, 81R10]

quantum field theory renormalization Feynman measure Hopf algebra Feynman diagram


Borcherds, Richard. Renormalization and quantum field theory. Algebra Number Theory 5 (2011), no. 5, 627--658. doi:10.2140/ant.2011.5.627.

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