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A study of the consistency between noncommutative quantum mechanics and Galilean isotropy

Jose Ignacio Usera
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Abstract

A demonstration is given that the simplest model of quantum mechanics formulated on a plane non-commutative geometry endowed with a Galilean symmetry group in which the position and linear momentum-variable commutators are first order in the dynamical variables (and thus constitute a true Lie algebra) is incompatible with the hypothesis of spacial isotropy.

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Jose Ignacio Usera. 2000-05-02. A study of the consistency between noncommutative quantum mechanics and Galilean isotropy. https://arxiv.org/abs/quant-ph/0005017

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