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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2007 |
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| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2007
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147208 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Vacuum Energy as Spectral Geometry / S.A. Fulling // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 60 назв. — англ. |
Репозитарії
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nasplib_isofts_kiev_ua-123456789-147208 |
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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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Vacuum Energy as Spectral Geometry |
| spellingShingle |
Vacuum Energy as Spectral Geometry Fulling, S.A. |
| title_short |
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 |
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vacuum energy as spectral geometry |
| author |
Fulling, S.A. |
| author_facet |
Fulling, S.A. |
| publishDate |
2007 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147208 |
| citation_txt |
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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AT fullingsa vacuumenergyasspectralgeometry |
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2025-12-07T21:00:32Z |
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2025-12-07T21:00:32Z |
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1850884732803350528 |