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

Carles Batlle ; Joaquim Gomis ; Kiyoshi Kamimura

Symmetry, integrability and geometry: methods and applications, Tome 10 (2014)

Résumé

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.

Détail

Keywords: non-commutative plane; Schrödinger equation; Schrödinger symmetries; higher spin symmetries.

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