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arXiv · 1404.2550

Conserved symmetries in noncommutative quantum mechanics

V. G. Kupriyanov
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Abstract

We consider a problem of the consistent deformation of physical system introducing a new features, but preserving its fundamental properties. In particular, we study how to implement the noncommutativity of space-time without violation of the rotational symmetry in quantum mechanics or the Lorentz symmetry in f{i}eld theory. Since the canonical (Moyal) noncommutativity breaks the above symmetries one should work with more general case of coordinate-dependent noncommutative spaces, when the commutator between coordinates is a function of these coordinates. F{i}rst we describe in general lines how to construct the quantum mechanics on coordinate-dependent noncommutative spaces. Then we consider the particular examples: the Hydrogen atom on rotationally invariant noncommutative space and the Dirac equation on covariant noncommutative space-time.

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V. G. Kupriyanov. 2014-04-09. Conserved symmetries in noncommutative quantum mechanics. https://doi.org/10.1002/prop.201400016

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