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Quantum Dynamics on the Worldvolume from Classical su(n) Cohomology
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2008, том 4
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Quantum Dynamics on the Worldvolume from Classical su(n) Cohomology
Інший ID:
2000 Mathematics Subject Classification: 81T30; 17B56
Посилання:
Quantum Dynamics on the Worldvolume from Classical su(n) Cohomology / J.M. Isidro, P. Fernández de Córdoba // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 20 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on Deformation Quantization. It is a great pleasure for J.M.I. to thank Max-Planck-Institut f¨ur Gravitationsphysik, AlbertEinstein-Institut, Golm (Germany) for hospitality during the preparation of this work. The authors thank Generalitat Valenciana (Spain) for financial support.
Дата:
2008
Переглядів:
455
Завантажень:
247
Анотація:
A key symmetry of classical p-branes is invariance under worldvolume diffeomorphisms. Under the assumption that the worldvolume, at fixed values of the time, is a compact, quantisable Kähler manifold, we prove that the Lie algebra of volume-preserving diffeomorphisms of the worldvolume can be approximated by su(n), for n → ∞. We also prove, under the same assumptions regarding the worldvolume at fixed time, that classical Nambu brackets on the worldvolume are quantised by the multibrackets corresponding to cocycles in the cohomology of the Lie algebra su(n).
