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Symmetries of the Free Schrödinger Equation in the Non-Commutative Plane

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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Main Authors: Batlle, C., Gomis, J., Kamimura, K.
Format: Article
Language:English
Published: Інститут математики НАН України 2014
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/146844
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spelling 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
work_keys_str_mv AT batllec symmetriesofthefreeschrodingerequationinthenoncommutativeplane
AT gomisj symmetriesofthefreeschrodingerequationinthenoncommutativeplane
AT kamimurak symmetriesofthefreeschrodingerequationinthenoncommutativeplane
first_indexed 2023-05-20T17:25:47Z
last_indexed 2023-05-20T17:25:47Z
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