A Dispersion Relation for the Density of States With Application to the Casimir Effect

Details A Dispersion Relation for the Density of States With Application to the Casimir Effect A Dispersion Relation for the Density of States With Application to the Casimir Effect

2010-11-21

arxiv.org/abs/1011.4659v1

Annals Phys.326:1536-1547,2011

Physics

Quantum Physics

Scientific paper

10.1016/j.aop.2010.12.012

The trace of a function of a Schrodinger operator minus the same for the Laplacian can be expressed in terms of the determinant of its scattering matrix. The naive formula for this determinant is divergent. Using a dispersion relation, we find another expression for it which is convergent, but needs one piece of information beyond the scattering matrix. Except for this `anomaly', we can express the Casimir energy of a compact body in terms of its optical scattering matrix, without assuming any rotational symmetry for its shape.

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