Pullback Coherent States, Squeezed States and Quantization
In this semi-expository paper, we define certain Rawnsley-type coherent and squeezed states on an integral Kähler manifold (after possibly removing a set of measure zero) and show that they satisfy some properties which are akin to the maximal likelihood property, reproducing kernel property, genera...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2022 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2022
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211640 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Pullback Coherent States, Squeezed States and Quantization. Rukmini Dey and Kohinoor Ghosh. SIGMA 18 (2022), 028, 14 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862746205636788224 |
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| author | Dey, Rukmini Ghosh, Kohinoor |
| author_facet | Dey, Rukmini Ghosh, Kohinoor |
| citation_txt | Pullback Coherent States, Squeezed States and Quantization. Rukmini Dey and Kohinoor Ghosh. SIGMA 18 (2022), 028, 14 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this semi-expository paper, we define certain Rawnsley-type coherent and squeezed states on an integral Kähler manifold (after possibly removing a set of measure zero) and show that they satisfy some properties which are akin to the maximal likelihood property, reproducing kernel property, generalised resolution of identity property, and overcompleteness. This is a generalization of a result by Spera. Next, we define the Rawnsley-type pullback coherent and squeezed states on a smooth compact manifold (after possibly removing a set of measure zero) and show that they satisfy similar properties. Finally, we show a Berezin-type quantization involving certain operators acting on a Hilbert space on a compact smooth totally real embedded submanifold of of real dimension , where is an open set in ℂPⁿ. Any other submanifold for which the criterion of the identity theorem holds exhibits this type of Berezin quantization. Also, this type of quantization holds for totally real submanifolds of real dimension of a general homogeneous Kähler manifold of real dimension 2 for which Berezin quantization exists. In the appendix, we review the Rawnsley and generalized Perelomov coherent states on ℂPⁿ (which is a coadjoint orbit) and the fact that these two types of coherent states coincide.
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| first_indexed | 2026-04-17T19:13:34Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-211640 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-04-17T19:13:34Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Dey, Rukmini Ghosh, Kohinoor 2026-01-07T13:43:20Z 2022 Pullback Coherent States, Squeezed States and Quantization. Rukmini Dey and Kohinoor Ghosh. SIGMA 18 (2022), 028, 14 pages 1815-0659 2020 Mathematics Subject Classification: 53D50; 53D55 arXiv:2108.08082 https://nasplib.isofts.kiev.ua/handle/123456789/211640 https://doi.org/10.3842/SIGMA.2022.028 In this semi-expository paper, we define certain Rawnsley-type coherent and squeezed states on an integral Kähler manifold (after possibly removing a set of measure zero) and show that they satisfy some properties which are akin to the maximal likelihood property, reproducing kernel property, generalised resolution of identity property, and overcompleteness. This is a generalization of a result by Spera. Next, we define the Rawnsley-type pullback coherent and squeezed states on a smooth compact manifold (after possibly removing a set of measure zero) and show that they satisfy similar properties. Finally, we show a Berezin-type quantization involving certain operators acting on a Hilbert space on a compact smooth totally real embedded submanifold of of real dimension , where is an open set in ℂPⁿ. Any other submanifold for which the criterion of the identity theorem holds exhibits this type of Berezin quantization. Also, this type of quantization holds for totally real submanifolds of real dimension of a general homogeneous Kähler manifold of real dimension 2 for which Berezin quantization exists. In the appendix, we review the Rawnsley and generalized Perelomov coherent states on ℂPⁿ (which is a coadjoint orbit) and the fact that these two types of coherent states coincide. The authors would like to thank Gautam Bharali (IISc, Bangalore) and Mahan Mj (TIFR, Mumbai) for the useful discussions on the theory of totally real submanifolds in several complex variables and Proposition 2.3. They would like to thank the anonymous referees for their valuable suggestions for improvement of the paper. Rukmini Dey acknowledges support from the project RTI4001, Department of Atomic Energy, Government of India, and support from grant CRG/2018/002835, Science and Engineering Research Board, Government of India. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Pullback Coherent States, Squeezed States and Quantization Article published earlier |
| spellingShingle | Pullback Coherent States, Squeezed States and Quantization Dey, Rukmini Ghosh, Kohinoor |
| title | Pullback Coherent States, Squeezed States and Quantization |
| title_full | Pullback Coherent States, Squeezed States and Quantization |
| title_fullStr | Pullback Coherent States, Squeezed States and Quantization |
| title_full_unstemmed | Pullback Coherent States, Squeezed States and Quantization |
| title_short | Pullback Coherent States, Squeezed States and Quantization |
| title_sort | pullback coherent states, squeezed states and quantization |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211640 |
| work_keys_str_mv | AT deyrukmini pullbackcoherentstatessqueezedstatesandquantization AT ghoshkohinoor pullbackcoherentstatessqueezedstatesandquantization |