Elsevier

Nuclear Physics B

Volume 371, Issues 1–2, 2 March 1992, Pages 353-414
Nuclear Physics B

Differential regularization and renormalization: a new method of calculation in quantum field theory

https://doi.org/10.1016/0550-3213(92)90240-CGet rights and content

Abstract

Most primitively divergent Feynman diagrams are well defined in x-space but too singular at short distances for transformation to p-space. A new method of regularization is developed in which singular functions are written as derivatives of less singular functions which contain a logarithmic mass scale. The Fourier transform is then defined by formal integration by parts. The procedure is extended to graphs with divergent subgraphs. No explicit cutoff or counter-terms are required, and the method automatically delivers renormalized amplitudes which satisfy Callan-Symanzik equations. These features are thoroughly explored in massless φ4 theory through 3-loop order, and the method yields explicit functional forms for all amplitudes with less difficulty than conventional methods which use dimensional regularization in p-space. The procedure also appears to be compatible with gauge invariance and the chiral structure of the standard model. This aspect is tested in extensive 1-loop calculations which include the Ward identity in quantum electrodynamics, the chiral anomaly, and the background field algorithm in non-abelian gauge theories.

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This work is supported in part by funds provided by the US Department of Energy (DOE) under contract #DE-AC02-76ER03069, the National Science Foundation under grant #87-08447, and CICYT.

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