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Advances in Mathematical Physics
Volume 2016, Article ID 5739410, 7 pages
http://dx.doi.org/10.1155/2016/5739410
Research Article

Higher Spin Symmetries of the Free Schrödinger Equation

Facultad de Ingeniera y Tecnología, Universidad San Sebastián, General Lagos 1163, 5110693 Valdivia, Chile

Received 20 April 2016; Accepted 26 July 2016

Academic Editor: Angel Ballesteros

Copyright © 2016 Mauricio Valenzuela. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

It is shown that the Schrödinger symmetry algebra of a free particle in spatial dimensions can be embedded into a representation of the higher spin algebra. The latter spans an infinite dimensional algebra of higher-order symmetry generators of the free Schrödinger equation. An explicit representation of the maximal finite dimensional subalgebra of the higher spin algebra is given in terms of nonrelativistic generators. We show also how to convert Vasiliev’s equations into an explicit nonrelativistic covariant form, such that they might apply to nonrelativistic systems. Our procedure reveals that the space of solutions of the Schrödinger equation can be regarded also as a supersymmetric module.