Dimensional regularization and renormalization of QED

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Dec 1990 English Publisher:Springer Science and Business Media LLCJournal:Communications in Mathematical Physics, volume 134, pages 433-466 (issn: 0010-3616, eissn: 1432-0916,

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Authors: Rosen, Lon; Wright, Jill D.;

doi: 10.1007/bf02098441

Dimensional regularization and renormalization of QED

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Abstract

The tree expansion method of renormalization [see e.g. \textit{G. Gallavotti}, Rev. Mod. Phys. 57, 471-562 (1985)] has been applied to QED by \textit{J. Feldman}, \textit{T. Hurd}, and the authors [QED: A proof of renormalizability. Lect. Notes Phys. 312 (1988)]. The purpose of the present paper is to replace the loop regularization used there, with an x-space formulation of dimensional regularization that is compatible with the tree expansion. Renormalization is achieved by subtraction of Lagrangian counterterms determined through the tree expansion, so does not entail a knowledge of the meromorphic structure of the graph as a function of dimension. This renormalization procedure respects the Ward identities, and the counterterms required are gauge invariant.

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Keywords

Applications of global analysis to the sciences, dimensional regularization, Applications of PDEs on manifolds, gauge invariant renormalization, 81V10, 81T15, tree expansion, Electromagnetic interaction; quantum electrodynamics, Perturbative methods of renormalization applied to problems in quantum field theory

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