A Dispersion Relation for the Density of States With Application to the Casimir Effect
Quantum Physics
2011-07-13 v1 High Energy Physics - Theory
Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.1011.4659,
title = {A Dispersion Relation for the Density of States With Application to the Casimir Effect},
author = {S. G. Rajeev},
journal= {arXiv preprint arXiv:1011.4659},
year = {2011}
}