Metaplectic-c Quantomorphisms
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Metaplectic-c Quantomorphisms
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| Creator |
Vaughan, J.
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| Description |
In the classical Kostant-Souriau prequantization procedure, the Poisson algebra of a symplectic manifold (M,ω) is realized as the space of infinitesimal quantomorphisms of the prequantization circle bundle. Robinson and Rawnsley developed an alternative to the Kostant-Souriau quantization process in which the prequantization circle bundle and metaplectic structure for (M,ω) are replaced by a metaplectic-c prequantization. They proved that metaplectic-c quantization can be applied to a larger class of manifolds than the classical recipe. This paper presents a definition for a metaplectic-c quantomorphism, which is a diffeomorphism of metaplectic-c prequantizations that preserves all of their structures. Since the structure of a metaplectic-c prequantization is more complicated than that of a circle bundle, we find that the definition must include an extra condition that does not have an analogue in the Kostant-Souriau case. We then define an infinitesimal quantomorphism to be a vector field whose flow consists of metaplectic-c quantomorphisms, and prove that the space of infinitesimal metaplectic-c quantomorphisms exhibits all of the same properties that are seen for the infinitesimal quantomorphisms of a prequantization circle bundle. In particular, this space is isomorphic to the Poisson algebra C∞(M).
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| Date |
2019-02-12T18:24:33Z
2019-02-12T18:24:33Z 2015 |
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| Type |
Article
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| Identifier |
Metaplectic-c Quantomorphisms / J. Vaughan // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 6 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 53D50; 81S10 DOI:10.3842/SIGMA.2015.025 http://dspace.nbuv.gov.ua/handle/123456789/147006 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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