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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| Дата: | 2014 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2014
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.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| id |
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irk-123456789-1468442019-02-12T01:23:55Z Symmetries of the Free Schrödinger Equation in the Non-Commutative Plane Batlle, C. Gomis, J. Kamimura, K. 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. 2014 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/146844 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 |
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. |
| format |
Article |
| author |
Batlle, C. Gomis, J. Kamimura, K. |
| spellingShingle |
Batlle, C. Gomis, J. Kamimura, K. Symmetries of the Free Schrödinger Equation in the Non-Commutative Plane Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Batlle, C. Gomis, J. Kamimura, K. |
| author_sort |
Batlle, C. |
| title |
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_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_sort |
symmetries of the free schrödinger equation in the non-commutative plane |
| publisher |
Інститут математики НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146844 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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AT batllec symmetriesofthefreeschrodingerequationinthenoncommutativeplane AT gomisj symmetriesofthefreeschrodingerequationinthenoncommutativeplane AT kamimurak symmetriesofthefreeschrodingerequationinthenoncommutativeplane |
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2023-05-20T17:25:47Z |
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2023-05-20T17:25:47Z |
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