A Dynamical Formulation of the Aharonov-bohm Effect

In 1969 Aharonov, Pend leton and Petersen introduced a new dynamical variable, the modular momentum, and discussed how several nonlDcal interactions could be characterized as resulting from its exchange. In this paper we review and extend their approach by applying it to the Aharonov~Bohm effect with an electromagnetic scalar potential. First we review the nonclassical nature of the effect, showing that the interaction involved does not change the linear momentum of any particle creating the interference pattern. We then use the modular momentum to describe the interaction in the Heisenberg picture. Studying the equation of motion for the motiular momentum, we prove the assertion of Aharonov et al. that modular momentum provides a dynamical description of the Aharonov-Boitm effect.