Vol. 5, No. 5, 2011

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Renormalization and quantum field theory

Richard E. Borcherds

Vol. 5 (2011), No. 5, 627–658

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.

quantum field theory, renormalization, Feynman measure, Hopf algebra, Feynman diagram
Mathematical Subject Classification 2000
Primary: 22E70
Received: 23 August 2010
Revised: 18 February 2011
Accepted: 24 April 2011
Published: 23 January 2012
Richard E. Borcherds
Department of Mathematics
University of California
Berkeley, CA 94720-3840
United States