The ESAB effect and the physical meaning of the vector potential

This paper deals with the so-called AB effect — AB stands for the names of the two physicists Y. Aharonov and D. Bohm — which has received new attention during the last decade, especially concerning its physical meaning. This effect should be referred by the acronym ESAB in order to recognize the pioneering work of W. Ehrenberg and R. Siday. Here we review the role of the electromagnetic potential in the interference phenomenon with charged particles and we recall that such a potential is never unambiguously defined since it depends on the choice of an arbitrary gauge. Therefore, it cannot play a primary role with respect to the electromagnetic field from which it is derived. However this does not rule out its great interest in theoretical physics. Indeed, it appears naturally when defining important quantities, such as the Lagrangian, the linear momentum, and the Hamiltonian, both in classical and quantum physics. By referring to a large panel of published experimental tests of the ESAB effect, we argue that only a pantopical point of view, i.e. rejecting the hypothesis of locality, can account for the behavior of an electron (or any charge) in an interferometer and its interaction with an electromagnetic field.