ua nt - p h / 05 03 21 2 v 1 2 8 M ar 2 00 5 On the Electric Charge Quantization from the Aharonov - Bohm Potential

The purpose of this paper is to show that we can define different vector potentials in the problems of Aharonov-Bohm type, in such a way that they give the same physical results as the one originally proposed by Aharonov and Bohm, except in the regions of space where the fields become singular. We argue that a modified quantization condition comes out for the electric charge that may open up the way for the understanding of fractional charges. One does not need any longer to rely on the existence of a magnetic monopole to justify electric charge quantization. The main goal of this paper is to show that, even in a quantum-mechanical context, we can take an Aharonov-Bohm-like potential as a gauge field, once we consider some restrictions on these gauge potentials, and, as a consequance, we are led to a quantization condition for the electric charge which does not involve the existence of magnetic monopoles and which is in agreement with the fractional character of quark charges and the existence of anti-particles. Before start discussing electric charge quantization with no appeal to monopoles, let us briefly recall the main aspects of Dirac's quantization, which intrinsically involves the existence of magnetic monopoles. To describe the field strength of a point-like magnetic monopole g, Dirac used the vector potential of a so-called Dirac's string [1, 2], which, if considered to be lying along the z < 0 semi-axis, gives the vector potential A I = g 1 − cos θ r sin θ ˆ φ , (1) where we used spherical coordinates where φ is the azimuthal angle. With this description, Dirac avoided the introduction of a scalar potential of magnetic nature and, consequently, the trouble of establishing an electrodynamics with a pair of four potentials [3]. Even so, expression