Maximally localized states and causality in noncommutative quantum theories

We give simple representations for quantum theories in which the position commutators are nonvanishing 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 noncommutation relations concern positions only. An interpretation of the wave function in this noncommutative geometry is suggested. We also analyze higher dimensional cases. A possible incidence on the causality issue for a quantum field theory with a noncommutating time is sketched