Generally covariant quantum mechanics on noncommutative configuration spaces

Details Generally covariant quantum mechanics on noncommutative configuration spaces Generally covariant quantum mechanics on noncommutative configuration spaces

2007-08-02

arxiv.org/abs/0708.0388v1

Physics

Mathematical Physics

20 pages

Scientific paper

10.1063/1.2804075

We generalize the previously given algebraic version of "Feynman's proof of Maxwell's equations" to noncommutative configuration spaces. By doing so, we also obtain an axiomatic formulation of nonrelativistic quantum mechanics over such spaces, which, in contrast to most examples discussed in the literature, does not rely on a distinguished set of coordinates. We give a detailed account of several examples, e.g., of nonabelian Yang-Mills theories, and of noncommutative tori. Moreover we, examine models over the Moyal-deformed plane. Assuming the conservation of electrical charges, we show that in this case the canonical uncertainty relation [x_k, \dot{x}_l] = ig_{kl} with metric g_{kl} is only consistent if g_{kl} is constant.

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