Renormalization and quantum field theory

Borcherds, Richard

doi:10.2140/ant.2011.5.627

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Renormalization and quantum field theory

Richard E. Borcherds

Vol. 5 (2011), No. 5, 627–658

DOI: 10.2140/ant.2011.5.627

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.

Keywords

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

Mathematical Subject Classification 2000

Primary: 22E70

Milestones

Received: 23 August 2010

Revised: 18 February 2011

Accepted: 24 April 2011

Published: 23 January 2012

Authors

Richard E. Borcherds
Department of Mathematics University of California Berkeley, CA 94720-3840 United States

Vol. 5, No. 5, 2011