Casimir Effects in Renormalizable Quantum Field Theories

Details Casimir Effects in Renormalizable Quantum Field Theories Casimir Effects in Renormalizable Quantum Field Theories

2002-01-18

arxiv.org/abs/hep-th/0201148v1

Int.J.Mod.Phys. A17 (2002) 846-869

Physics

High Energy Physics

High Energy Physics - Theory

27 pp., 11 EPS figures, LaTeX using ijmpa1.sty; email correspondence to R.L. Jaffe <jaffe@mit.edu> ; based on talks presented

Scientific paper

10.1142/S0217751X02010224

We review the framework we and our collaborators have developed for the study of one-loop quantum corrections to extended field configurations in renormalizable quantum field theories. We work in the continuum, transforming the standard Casimir sum over modes into a sum over bound states and an integral over scattering states weighted by the density of states. We express the density of states in terms of phase shifts, allowing us to extract divergences by identifying Born approximations to the phase shifts with low order Feynman diagrams. Once isolated in Feynman diagrams, the divergences are canceled against standard counterterms. Thus regulated, the Casimir sum is highly convergent and amenable to numerical computation. Our methods have numerous applications to the theory of solitons, membranes, and quantum field theories in strong external fields or subject to boundary conditions.

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