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Abstract: The Casimir force due to a massless scalar field satisfying Dirichletboundary conditions may attract or repel a piston in the neck of a flask-likecontainer. Using the world-line formalism this behavior is related to thecompeting contribution to the interaction energy of two types of Brownianbridges. It qualitatively is also expected from attractive long-range two-bodyforces between constituents of the boundary. A geometric subtraction scheme ispresented that avoids divergent contributions to the interaction energy andclassifies the Brownian bridges that contribute to the force. These are all offinite length and the Casimir force can be analyzed and in principle accuratelycomputed without resorting to regularization or analytic continuation. Theworld-line analysis is robust with respect to variations in the shape of thepiston and the flask and the analogy with long-range forces suggests thatneutral atoms and particles are also drawn into open-ended pipes ornano-tubes by Casimir forces of electromagnetic origin.

Autor: Martin Schaden

Fuente: https://arxiv.org/

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