Natural and Projectively Invariant Quantizations on Supermanifolds
The existence of a natural and projectively invariant quantization in the sense of P. Lecomte [Progr. Theoret. Phys. Suppl. (2001), no. 144, 125-132] was proved by M. Bordemann [math.DG/0208171], using the framework of Thomas-Whitehead connections. We extend the problem to the context of supermanifo...
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| Дата: | 2011 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2011
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146803 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Natural and Projectively Invariant Quantizations on Supermanifolds / T. Leuther, F. Radoux // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 16 назв. — англ. |
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irk-123456789-1468032019-02-12T01:24:23Z Natural and Projectively Invariant Quantizations on Supermanifolds Leuther, T. Radoux, F. The existence of a natural and projectively invariant quantization in the sense of P. Lecomte [Progr. Theoret. Phys. Suppl. (2001), no. 144, 125-132] was proved by M. Bordemann [math.DG/0208171], using the framework of Thomas-Whitehead connections. We extend the problem to the context of supermanifolds and adapt M. Bordemann's method in order to solve it. The obtained quantization appears as the natural globalization of the pgl(n+1|m)-equivariant quantization on Rn|m constructed by P. Mathonet and F. Radoux in [arXiv:1003.3320]. Our quantization is also a prolongation to arbitrary degree symbols of the projectively invariant quantization constructed by J. George in [arXiv:0909.5419] for symbols of degree two. 2011 Article Natural and Projectively Invariant Quantizations on Supermanifolds / T. Leuther, F. Radoux // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 16 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53B05; 53B10; 53D50; 58A50 DOI:10.3842/SIGMA.2011.034 http://dspace.nbuv.gov.ua/handle/123456789/146803 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
The existence of a natural and projectively invariant quantization in the sense of P. Lecomte [Progr. Theoret. Phys. Suppl. (2001), no. 144, 125-132] was proved by M. Bordemann [math.DG/0208171], using the framework of Thomas-Whitehead connections. We extend the problem to the context of supermanifolds and adapt M. Bordemann's method in order to solve it. The obtained quantization appears as the natural globalization of the pgl(n+1|m)-equivariant quantization on Rn|m constructed by P. Mathonet and F. Radoux in [arXiv:1003.3320]. Our quantization is also a prolongation to arbitrary degree symbols of the projectively invariant quantization constructed by J. George in [arXiv:0909.5419] for symbols of degree two. |
| format |
Article |
| author |
Leuther, T. Radoux, F. |
| spellingShingle |
Leuther, T. Radoux, F. Natural and Projectively Invariant Quantizations on Supermanifolds Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Leuther, T. Radoux, F. |
| author_sort |
Leuther, T. |
| title |
Natural and Projectively Invariant Quantizations on Supermanifolds |
| title_short |
Natural and Projectively Invariant Quantizations on Supermanifolds |
| title_full |
Natural and Projectively Invariant Quantizations on Supermanifolds |
| title_fullStr |
Natural and Projectively Invariant Quantizations on Supermanifolds |
| title_full_unstemmed |
Natural and Projectively Invariant Quantizations on Supermanifolds |
| title_sort |
natural and projectively invariant quantizations on supermanifolds |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146803 |
| citation_txt |
Natural and Projectively Invariant Quantizations on Supermanifolds / T. Leuther, F. Radoux // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 16 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT leuthert naturalandprojectivelyinvariantquantizationsonsupermanifolds AT radouxf naturalandprojectivelyinvariantquantizationsonsupermanifolds |
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2023-05-20T17:25:51Z |
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2023-05-20T17:25:51Z |
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1796153275889745920 |