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

被引：3

作者：

Batlle, Carles ^{[1
,2
]}

Gomis, Jaoquim ^{[3
,4
]}

Kamimura, Kiyoshi ^{[5
]}

机构：

[1] Univ Politecn Cataluna, BarcelonaTech, EPSEVG, Dept Matemat Aplicada 4, Vilanova I La Geltru 08800, Spain

[2] Univ Politecn Cataluna, BarcelonaTech, EPSEVG, Inst Org & Control, Vilanova I La Geltru 08800, Spain

[3] Univ Barcelona, Dept Estruct & Constituents Mat, E-08028 Barcelona, Spain

[4] Univ Barcelona, Inst Ciencies Cosmos, E-08028 Barcelona, Spain

[5] Toho Univ, Dept Phys, Chiba 2748510, Japan

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2014年 / 10卷

关键词：

non-commutative plane; Schrodinger equation; Schrodinger symmetries; higher spin symmetries; GALILEAN SYMMETRY; SCALE; TERM;

D O I：

10.3842/SIGMA.2014.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：15

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