Eur. Phys. J. C (2008) 55: 667-681
https://doi.org/10.1140/epjc/s10052-008-0614-6

Regular Article - Theoretical Physics

Implicit regularization beyond one-loop order: gauge field theories

¹ Federal University of Minas Gerais, Physics Department, ICEx, P.O. Box 702, 30.161-970, Belo Horizonte MG, Brazil
² Centro Federal de Educação Tecnológica – MG, Avenida Amazonas, 7675, 30510-000, Nova Gameleira, Belo Horizonte MG, Brazil

^* e-mail: edsondias@fisica.ufmg.br

Received: 27 March 2008
Published online: 17 May 2008

Abstract

We extend a constrained version of implicit regularization (CIR) beyond one-loop order for gauge field theories. In this framework, the ultraviolet content of the model is displayed in terms of momentum loop integrals order by order in perturbation theory for any Feynman diagram, while the Ward–Slavnov–Taylor identities are controlled by finite surface terms. To illustrate, we apply CIR to massless abelian gauge field theories (scalar and spinorial QED) to two-loop order and calculate the two-loop beta-function of spinorial QED.