Aharonov-Bohm effect on noncommutative plane: A coherent state approach

We formulate in a systematic manner the coherent state approach and apply it to study Aharonov-Bohm effect in the field theory context. Within this approach, we verify that the scattering amplitude is ultraviolet finite. Also, we prove that introduction of a quartic self-interaction for the scalar field allows to obtain a smooth commutative limit.