Symmetries of the Free Schrödinger Equation in the Non-Commutative Plane
We study all the symmetries of the free Schrödinger equation in the non-commutative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean boosts and momenta. These infinite high symmetrie...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2014 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2014
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/146844 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Symmetries of the Free Schrödinger Equation in the Non-Commutative Plane / C. Batlle, J. Gomis, K.Kamimura // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 25 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862598238632148992 |
|---|---|
| author | Batlle, C. Gomis, J. Kamimura, K. |
| author_facet | Batlle, C. Gomis, J. Kamimura, K. |
| citation_txt | Symmetries of the Free Schrödinger Equation in the Non-Commutative Plane / C. Batlle, J. Gomis, K.Kamimura // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 25 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We study all the symmetries of the free Schrödinger equation in the non-commutative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean boosts and momenta. These infinite high symmetries could be useful for constructing non-relativistic interacting higher spin theories. A finite-dimensional subalgebra is given by the Schrödinger algebra which, besides the Galilei generators, contains also the dilatation and the expansion. We consider the quantization of the symmetry generators in both the reduced and extended phase spaces, and discuss the relation between both approaches.
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| first_indexed | 2025-11-27T18:46:12Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146844 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-27T18:46:12Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Batlle, C. Gomis, J. Kamimura, K. 2019-02-11T17:07:27Z 2019-02-11T17:07:27Z 2014 Symmetries of the Free Schrödinger Equation in the Non-Commutative Plane / C. Batlle, J. Gomis, K.Kamimura // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 25 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81R60; 81S05; 83C65 DOI:10.3842/SIGMA.2014.011 https://nasplib.isofts.kiev.ua/handle/123456789/146844 We study all the symmetries of the free Schrödinger equation in the non-commutative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean boosts and momenta. These infinite high symmetries could be useful for constructing non-relativistic interacting higher spin theories. A finite-dimensional subalgebra is given by the Schrödinger algebra which, besides the Galilei generators, contains also the dilatation and the expansion. We consider the quantization of the symmetry generators in both the reduced and extended phase spaces, and discuss the relation between both approaches. This paper is a contribution to the Special Issue on Deformations of Space-Time and its Symmetries. The
 full collection is available at http://www.emis.de/journals/SIGMA/space-time.html.
 We thank Jorge Zanelli for collaboration in some parts of this work and Mikhail Plyushchay for
 reading the manuscript. We also thank Adolfo Azc´arraga and Jurek Lukierski for discussions,
 and Rabin Banerjee for letting us know about the results in [3]. CB was partially supported by
 Spanish Ministry of Economy and Competitiveness project DPI2011-25649. We also acknowledge
 partial financial support from projects FP2010-20807-C02-01, 2009SGR502 and CPAN
 Consolider CSD 2007-00042. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Symmetries of the Free Schrödinger Equation in the Non-Commutative Plane Article published earlier |
| spellingShingle | Symmetries of the Free Schrödinger Equation in the Non-Commutative Plane Batlle, C. Gomis, J. Kamimura, K. |
| title | Symmetries of the Free Schrödinger Equation in the Non-Commutative Plane |
| title_full | Symmetries of the Free Schrödinger Equation in the Non-Commutative Plane |
| title_fullStr | Symmetries of the Free Schrödinger Equation in the Non-Commutative Plane |
| title_full_unstemmed | Symmetries of the Free Schrödinger Equation in the Non-Commutative Plane |
| title_short | Symmetries of the Free Schrödinger Equation in the Non-Commutative Plane |
| title_sort | symmetries of the free schrödinger equation in the non-commutative plane |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146844 |
| work_keys_str_mv | AT batllec symmetriesofthefreeschrodingerequationinthenoncommutativeplane AT gomisj symmetriesofthefreeschrodingerequationinthenoncommutativeplane AT kamimurak symmetriesofthefreeschrodingerequationinthenoncommutativeplane |