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In a minimalistic view, the use of noncommutative coordinates can be seen just as a way to better express non-local interactions of a special kind: 1-particle solutions (wavefunctions) of the equation of motion in the presence of an external field may look simpler as functions of noncommutative coordinates.
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G. Fiore, “On second quantization on noncommutative spaces with twisted symmetries”, arXiv:0811.0773
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