Vacuum Energy as Spectral Geometry
arXiv:0706.2831 · doi:10.3842/SIGMA.2007.094
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.
This is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
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Cited by in corpus (5)
- A mathematical analysis of Casimir interactions I: The scalar field
- Ambiguities in the local thermal behavior of the scalar radiation in one-dimensional boxes
- Thermodynamics of the scalar radiation in the presence of a reflecting plane wall
- The Boundary-Integral Formulation and Multiple-Reflection Expansion for the Vacuum Energy of Quantum Graphs
- Vacuum energy density and pressure of a massive scalar field