The complex pre-potential and the Aharonov–Bohm effect

Abstract

The Aharonov–Bohm (AB) effect is traditionally attributed to the affect of the electromagnetic 4-potential A, even in regions where both the electric field and the magnetic field are zero. We argue that the quantity measured by AB experiments may be the difference in values of a multiple-valued complex function, which we call a pre-potential. The pre-potential is a combination of the two scalar potential functions introduced by Whittaker. We show that any electromagnetic field can be described by such a pre-potential, and give an explicit expression for the electromagnetic field tensor through this potential. The covariance of the pre-potential is explained. A program for deriving the AB effect from the pre-potential is proposed.