Metaplectic-c Quantomorphisms
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...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2015 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2015
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147006 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Metaplectic-c Quantomorphisms / J. Vaughan // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 6 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862714405218680832 |
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| author | Vaughan, J. |
| author_facet | Vaughan, J. |
| citation_txt | Metaplectic-c Quantomorphisms / J. Vaughan // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 6 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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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| first_indexed | 2025-12-07T17:50:30Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147006 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:50:30Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Vaughan, J. 2019-02-12T18:24:33Z 2019-02-12T18:24:33Z 2015 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 https://nasplib.isofts.kiev.ua/handle/123456789/147006 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). The author thanks Alejandro Uribe and Yael Karson for enlightening discussions. This work
 was funded in part by an NSERC scholarship. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Metaplectic-c Quantomorphisms Article published earlier |
| spellingShingle | Metaplectic-c Quantomorphisms Vaughan, J. |
| title | Metaplectic-c Quantomorphisms |
| title_full | Metaplectic-c Quantomorphisms |
| title_fullStr | Metaplectic-c Quantomorphisms |
| title_full_unstemmed | Metaplectic-c Quantomorphisms |
| title_short | Metaplectic-c Quantomorphisms |
| title_sort | metaplectic-c quantomorphisms |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147006 |
| work_keys_str_mv | AT vaughanj metaplecticcquantomorphisms |