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Symmetry, Integrability and Geometry: Methods and Applications, 2014, Volume 10, 011, 15 pp.
DOI: https://doi.org/10.3842/SIGMA.2014.011 (Mi sigma876) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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

Carles Batllea, Joaquim Gomisb, Kiyoshi Kamimurac

a Departament de Matemàtica Aplicada 4 and Institut d’Organització i Control, Universitat Politècnica de Catalunya - BarcelonaTech, EPSEVG, Av. V. Balaguer 1, 08800 Vilanova i la Geltrú, Spain
b Departament d’Estructura i Constituents de la Matèria and Institut de Ciències del Cosmos, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain
c Department of Physics, Toho University, Funabashi, Chiba 274-8510, Japan
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DOI: https://doi.org/10.3842/SIGMA.2014.011
Abstract: 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.
Keywords: non-commutative plane; Schrödinger equation; Schrödinger symmetries; higher spin symmetries.
Received: August 29, 2013; in final form January 29, 2014; Published online February 8, 2014
Bibliographic databases:
Document Type: Article
MSC: 81R60; 81S05; 83C65
Language: English
Citation: Carles Batlle, Joaquim Gomis, Kiyoshi Kamimura, “Symmetries of the Free Schrödinger Equation in the Non-Commutative Plane”, SIGMA, 10 (2014), 011, 15 pp.
Citation in format AMSBIB
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\by Carles~Batlle, Joaquim~Gomis, Kiyoshi~Kamimura
\paper Symmetries of the Free Schr\"odinger Equation in the Non-Commutative Plane
\jour SIGMA
\yr 2014
\vol 10
\papernumber 011
\totalpages 15
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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