Higher-spin symmetries of the free Schrodinger equation

Details Higher-spin symmetries of the free Schrodinger equation Higher-spin symmetries of the free Schrodinger equation

2009-12-04

arxiv.org/abs/0912.0789v4

Physics

High Energy Physics

High Energy Physics - Theory

The statement on the non-relativistic covariance of Vasiliev higher spin theory is made more explicit

Scientific paper

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 the Vasiliev equations into an explicit non-relativistic covariant form, such that they may 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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