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arXiv · hep-th/0402220

Space-Time Noncommutativity from Particle Mechanics

A. Pinzul·A. Stern
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Abstract

We exploit the reparametrization symmetry of a relativistic free particle to impose a gauge condition which upon quantization implies space-time noncommutativity. We show that there is an algebraic map from this gauge back to the standard `commuting' gauge. Therefore the Poisson algebra, and the resulting quantum theory, are identical in the two gauges. The only difference is in the interpretation of space-time coordinates. The procedure is repeated for the case of a coupling with a constant electromagnetic field, where the reparametrization symmetry is preserved. For more arbitrary interactions, we show that standard dynamical system can be rendered noncommutative in space and time by a simple change of variables.

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A. Pinzul, A. Stern. 2004-03-05. Space-Time Noncommutativity from Particle Mechanics. https://doi.org/10.1016/j.physletb.2004.04.079

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