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arXiv · hep-th/0106018

Maximally localized states and causality in non commutative quantum theories

M. Lubo
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Abstract

We give simple representations for quantum theories in which the position commutators are non vanishing constants. A particular representation reproduces results found using the Moyal star product. The notion of exact localization being meaningless in these theories, we adapt the notion of ``maximally localized states'' developed in another context . We find that gaussian functions play this role in a 2+1 dimensional model in which the non commutation relations concern positions only. An interpretation of the wave function in this non commutative geometry is suggested. We also analyze higher dimensional cases. A possible incidence on the causality issue for a Q.F.T with a non commuting time is sketched.

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M. Lubo. 2001-12-10. Maximally localized states and causality in non commutative quantum theories. https://doi.org/10.1103/physrevd.65.066003

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