Vacuum Energy as Spectral Geometry
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 eigenvalu...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2007 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2007
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147208 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Vacuum Energy as Spectral Geometry / S.A. Fulling // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 60 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862749500696690688 |
|---|---|
| author | Fulling, S.A. |
| author_facet | Fulling, S.A. |
| citation_txt | Vacuum Energy as Spectral Geometry / S.A. Fulling // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 60 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2025-12-07T21:00:32Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147208 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:00:32Z |
| publishDate | 2007 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Fulling, S.A. 2019-02-13T19:05:47Z 2019-02-13T19:05:47Z 2007 Vacuum Energy as Spectral Geometry / S.A. Fulling // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 60 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 34B27; 81Q10; 58J50 https://nasplib.isofts.kiev.ua/handle/123456789/147208 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 paper is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson. This work has been supported by the National Science Foundation under Grants DMS-0405806 and PHY-0554849. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Vacuum Energy as Spectral Geometry Article published earlier |
| spellingShingle | Vacuum Energy as Spectral Geometry Fulling, S.A. |
| title | Vacuum Energy as Spectral Geometry |
| title_full | Vacuum Energy as Spectral Geometry |
| title_fullStr | Vacuum Energy as Spectral Geometry |
| title_full_unstemmed | Vacuum Energy as Spectral Geometry |
| title_short | Vacuum Energy as Spectral Geometry |
| title_sort | vacuum energy as spectral geometry |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147208 |
| work_keys_str_mv | AT fullingsa vacuumenergyasspectralgeometry |