Vacuum Energy as Spectral Geometry

Details Vacuum Energy as Spectral Geometry Vacuum Energy as Spectral Geometry

2007-06-19

arxiv.org/abs/0706.2831v2

SIGMA 3 (2007), 094, 23 pages

Physics

Mathematical Physics

This is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson, published in

Scientific paper

10.3842/SIGMA.2007.094

Quantum vacuum energy (Casimir energy) is reviewed for a mathematical audience as a topic in spectral theory. Then some one-dimensional systems are solved exactly, in terms of closed classical paths and periodic orbits. The relations among local spectral densities, energy densities, global eigenvalue densities, and total energies are demonstrated. This material provides background and motivation for the treatment of higher-dimensional systems (self-adjoint second-order partial differential operators) by semiclassical approximation and other methods.

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