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Casimir Effect on the Worldline

Holger Gies·Kurt Langfeld·Laurent Moyaerts
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Abstract

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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Holger Gies, Kurt Langfeld, Laurent Moyaerts. 2003-06-13. Casimir Effect on the Worldline. https://doi.org/10.1088/1126-6708%2F2003%2F06%2F018

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