Stochastic quantization and Casimir forces: pistons of arbitrary cross section

Abstract

Recently, a method based on stochastic quantization has been proposed to compute the Casimir force and its fluctuations in arbitrary geometries. It relies on the spectral decomposition of the Laplace operator in the given geometry. Both quantum and thermal fluctuations were considered. Here we use this method to compute the Casimir force on the plates of a finite piston of arbitrary cross section. Asymptotic expressions valid at low and high temperatures, as well as short and long distances are obtained. The case of a piston with triangular cross section is analyzed in detail. The regularization of the divergent stress tensor is described.