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Vacuum Energy as Spectral Geometry
Репозиторій DSpace/Manakin
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3
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- Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3, випуск за цей рік
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Vacuum Energy as Spectral Geometry
Інший ID:
2000 Mathematics Subject Classification: 34B27; 81Q10; 58J50
Посилання:
Vacuum Energy as Spectral Geometry / S.A. Fulling // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 60 назв. — англ.
Підтримка:
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.
Дата:
2007
Переглядів:
717
Завантажень:
269
Анотація:
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.
