Vacuum Energy as Spectral Geometry
Mathematical Physics
2008-04-25 v2 Differential Geometry
math.MP
Abstract
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.
Cite
@article{arxiv.0706.2831,
title = {Vacuum Energy as Spectral Geometry},
author = {Stephen A. Fulling},
journal= {arXiv preprint arXiv:0706.2831},
year = {2008}
}