Casimir Effect on the Worldline

Details Casimir Effect on the Worldline Casimir Effect on the Worldline

2003-03-31

arxiv.org/abs/hep-th/0303264v2

JHEP0306:018,2003

Physics

High Energy Physics

High Energy Physics - Theory

27 pages, 10 figures, Sect. 2.1 more self-contained, improved data for Fig. 6, minor corrections, new Refs, version to be publ

Scientific paper

10.1088/1126-6708/2003/06/018

We develop a method to compute the Casimir effect for arbitrary geometries. The method is based on the string-inspired worldline approach to quantum field theory and its numerical realization with Monte-Carlo techniques. Concentrating on Casimir forces between rigid bodies induced by a fluctuating scalar field, we test our method with the parallel-plate configuration. For the experimentally relevant sphere-plate configuration, we study curvature effects quantitatively and perform a comparison with the ``proximity force approximation'', which is the standard approximation technique. Sizable curvature effects are found for a distance-to-curvature-radius ratio of a/R >~ 0.02. Our method is embedded in renormalizable quantum field theory with a controlled treatment of the UV divergencies. As a technical by-product, we develop various efficient algorithms for generating closed-loop ensembles with Gaussian distribution.

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