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Renormalization and vacuum energy for an interacting scalar field in a delta-function potential

Lookup NU author(s): Professor David Toms

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Abstract

We study a self-interacting scalar field theory in the presence of a delta-function background potential. The role of surface interactions in obtaining a renormalizable theory is stressed and demonstrated by a two-loop calculation. The necessary counterterms are evaluated by adopting dimensional regularization and the background field method. We also calculate the effective potential for a complex scalar field in a non-simply connected spacetime in the presence of a delta-function potential. The effective potential is evaluated as a function of an arbitrary phase factor associated with the choice of boundary conditions in the non-simply connected spacetime. We obtain asymptotic expansions of the results for both large and small delta-function strengths, and stress how the non-analytic nature of the small strength result vitiates any analysis based on standard weak field perturbation theory. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker's 75th birthday devoted to 'Applications of zeta functions and other spectral functions in mathematics and physics'.

Publication metadata

Author(s): Toms DJ

Publication type: Article

Publication status: Published

Journal: Journal of Physics A: Mathematical and Theoretical

Year: 2012

Volume: 45

Issue: 37

Print publication date: 04/09/2012

ISSN (print): 1751-8113

ISSN (electronic): 1751-8121

Publisher: Institute of Physics Publishing Ltd.

URL: http://dx.doi.org/10.1088/1751-8113/45/37/374026

DOI: 10.1088/1751-8113/45/37/374026

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