Maximally localized states and causality in non commutative quantum theories

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.

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

References in corpus (3)

• The quantum structure of spacetime at the Planck scale and quantum fields
• New Tests of Lorentz Invariance Following from Observations of the Highest Energy Cosmic Gamma Rays
• Quantum Theories on Noncommutative Spaces with Nontrivial Topology: Aharonov-Bohm and Casimir Effects

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