Space-Time Noncommutativity from Particle Mechanics

Details Space-Time Noncommutativity from Particle Mechanics Space-Time Noncommutativity from Particle Mechanics

2004-02-26

arxiv.org/abs/hep-th/0402220v2

Phys.Lett. B593 (2004) 279-286

Physics

High Energy Physics

High Energy Physics - Theory

13 pp

Scientific paper

10.1016/j.physletb.2004.04.079

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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