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arXiv · 0912.0789

Higher-spin symmetries of the free Schrodinger equation

Mauricio Valenzuela
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Abstract

It is shown that the Schrodinger symmetry algebra of a free particle in d 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 Schrodinger equation. An explicit representation of the maximal finite dimensional subalgebra of the higher spin algebra is given in terms of non-relativistic generators. We show also how to convert Vasiliev's equations into an explicit non-relativistic covariant form, such that they might apply to non-relativistic systems. Our procedure reveals that the space of solutions of the Schrodinger equation can be regarded also as a supersymmetric module.

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Mauricio Valenzuela. 2009-12-04. Higher-spin symmetries of the free Schrodinger equation. https://arxiv.org/abs/0912.0789

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