Aharonov-Bohm Effect on Noncommutative Plane: A Coherent State Approach
  We apply the coherent state approach to study Aharonov-Bohm effect in the field theory context. We verify that, contrarily to the commutative result, the scattering amplitude is ultraviolet finite. However, we have logarithmic singularities as the noncommutative parameter tends to zero. Thus, the inclusion of a quartic self-interaction for the scalar field is necessary to obtain a smooth commutative limit. 
M. A. Anacleto, J. R. Nascimento, A. Yu. Petrov