Casimir effect on the worldline

We develop a method to compute the Casimir effect for arbitrary geometries.The method is based on the string-inspired worldline approach to quantum fieldtheory and its numerical realization with Monte-Carlo techniques. Concentratingon Casimir forces between rigid bodies induced by a fluctuating scalar field,we test our method with the parallel-plate configuration. For theexperimentally relevant sphere-plate configuration, we study curvature effectsquantitatively and perform a comparison with the ``proximity forceapproximation'', which is the standard approximation technique. Sizablecurvature 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 acontrolled treatment of the UV divergencies. As a technical by-product, wedevelop various efficient algorithms for generating closed-loop ensembles withGaussian distribution.Comment: 27 pages, 10 figures, Sect. 2.1 more self-contained, improved data for Fig. 6, minor corrections, new Refs, version to be published in JHE