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

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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.

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Institute of Mathematics of the National Academy of Sciences of Ukraine

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Symmetry Integrability and Geometry: Methods and Applications, 2014, vol. 10, p. 011

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Articles publicats en revistes (Física Quàntica i Astrofísica)

# metadata.dc.title[].value
Symmetries of the free Schrödinger equation in the non-commutative plane