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Symmetries of the free Schrödinger equation in the non-commutative plane
Batlle, C.; Gomis Torné, Joaquim; Kamimura, Kiyoshi
Universitat de Barcelona
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.
Equació de Schrödinger
Spin (Física nuclear)
Teoria quàntica
Schrödinger equation
Nuclear spin
Quantum theory
cc-by-nc-sa (c) Batlle, C. et al., 2014
Institute of Mathematics of the National Academy of Sciences of Ukraine

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