Symmetries of the free Schrödinger equation in the non-commutative plane

We study all the symmetries of the free Schrödinger equation in the non-commu- tative 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 symmetr...

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Detalhes bibliográficos
Autores: Batlle Arnau, Carles, Gomis Torné, Joaquim, Kamimura, Kiyoshi
Tipo de documento: artigo
Estado:Versão publicada
Data de publicação:2014
País:España
Recursos:Universidad de Barcelona
Repositório:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/54286
Acesso em linha:https://hdl.handle.net/2445/54286
Access Level:Acceso aberto
Palavra-chave:Equació de Schrödinger
Spin (Física nuclear)
Teoria quàntica
Schrödinger equation
Nuclear spin
Quantum theory
Descrição
Resumo:We study all the symmetries of the free Schrödinger equation in the non-commu- tative 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 Schröodinger 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.