Renormalization and vacuum energy for an interacting scalar field in a \delta-function potential
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.
Keywords
Cite
@article{arxiv.1204.3497,
title = {Renormalization and vacuum energy for an interacting scalar field in a \delta-function potential},
author = {David J. Toms},
journal= {arXiv preprint arXiv:1204.3497},
year = {2015}
}
Comments
To appear in the special issue of J. Phys. A to honour J. S. Dowker