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This article is cited in 9 scientific papers (total in 9 papers)
Vacuum Energy as Spectral Geometry
Stephen A. Fulling Department of Mathematics, Texas A\&M University, College Station, Texas, 77843-3368, USA
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.
Keywords:
Casimir; periodic orbit; energy density; cylinder kernel.
Received: June 21, 2007; in final form September 14, 2007; Published online September 26, 2007
Citation:
Stephen A. Fulling, “Vacuum Energy as Spectral Geometry”, SIGMA, 3 (2007), 094, 23 pp.
Linking options:
https://www.mathnet.ru/eng/sigma220 https://www.mathnet.ru/eng/sigma/v3/p94
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Abstract page: | 209 | Full-text PDF : | 60 | References: | 28 |
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