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arXiv · 1011.4659

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

S. G. Rajeev
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Abstract

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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S. G. Rajeev. 2010-11-21. A Dispersion Relation for the Density of States With Application to the Casimir Effect. https://doi.org/10.1016/j.aop.2010.12.012

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