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

We study all the symmetries of the free Schrodinger 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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Detalles Bibliográficos
Autores: Batlle Arnau, Carles|||0000-0002-6088-6187, Gomis, Jaoquim, Kamimura, kiyoshi
Tipo de recurso: artículo
Fecha de publicación:2014
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/23380
Acceso en línea:https://hdl.handle.net/2117/23380
https://dx.doi.org/10.3842/SIGMA.2014.011
Access Level:acceso abierto
Palabra clave:Schrödinger equation
Algebra
Mathematical physics
non-commutative plane
Schrodinger equation
Schrodinger symmetries
higher spin symmetries
PHENOMENOLOGICAL LAGRANGIANS
GALILEAN SYMMETRY
FIELD-THEORY
SCALE
SPACE
TERM
Schrödinger, Equació de
Àlgebra
Física matemàtica
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals
Descripción
Sumario:We study all the symmetries of the free Schrodinger 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 Schrodinger 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.