An exact evaluation of the Casimir energy in two planar models

S. G. Kamath

doi:10.1063/1.3192280

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arXiv · 0906.1641

An exact evaluation of the Casimir energy in two planar models

S. G. Kamath

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Abstract

The method of images is used to calculate the Casimir energy in Euclidean space with Dirichlet boundary conditions for two planar models, namely: i. the non-relativistic Landau problem for a charged particle of mass m for which - irrespective of the sign of the charge - the energy is negative, and ii. the model of a real, massive, noninteracting relativistic scalar field theory in 2 + 1 dimensions, for which the Casimir energy density is non-negative and is expressed in terms of the Lerch transcendent xxx and the polylogarithm xxx with 0 < xxx < 1 and n = 2, 3.

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S. G. Kamath. 2009-06-09. An exact evaluation of the Casimir energy in two planar models. https://doi.org/10.1063/1.3192280

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