Maximally localized states and causality in non commutative quantum theories

Details Maximally localized states and causality in non commutative quantum theories Maximally localized states and causality in non commutative quantum theories

2001-06-02

arxiv.org/abs/hep-th/0106018v2

Phys.Rev. D65 (2002) 066003

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, Revtex. The presentation has been improved, the subsection on high dimensions has been modified. This version will a

Scientific paper

10.1103/PhysRevD.65.066003

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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