Role of the nonlocality of the vector potential in the Aharonov–Bohm effect

Abstract

When the electromagnetic potentials are expressed in the Coulomb gauge in terms of the electric and magnetic fields rather than the sources responsible for these fields they have a simple form that is non-local i.e. the potentials depend on the fields at every point in space. It is this non-locality of classical electrodynamics that is primarily responsible for the puzzle associated with the static Aharonov-Bohm effect: that its interference pattern is affected by fields in a region of space that the electron beam never enters. Non-locality of the vector potential A.M.Stewart arXiv2014v5 25/4/14

A Non-Local Action for Electrodynamics: Duality Symmetry and the Aharonov-Bohm Effect, Revisited

“…Therefore, the non-locality suggested by the standard derivation of the magnetic AB effect appears naturally in the non-local prescription of electrodynamics described here. While the result (3.8) can be derived by simply applying the Coulomb gauge on (1.8) [26], we stress how here it has really been proven from a more fundamental action (3.1), and not from an arbitrary choice of gauge. Figure 1.…”

Decoupled Potential Integral Equations for Electromagnetic Scattering From Dielectric Objects

“…The formulation and discussion presented later is under this assumption for, largely due to simplicity. Though solutions match the Maxwell's equation with scalar and potentials being auxiliary quantities, effects of the assumption on the true vector or scalar potential problem is not known and worth being studied requiring more rigorous physical analysis, i.e., asking a more fundamental questionwhether a description using scalar-vector potential A−φ rather than E − H is possible [26], [27].…”

Does the Helmholtz theorem of vector decomposition apply to the wave fields of electromagnetic radiation?

“…Next we examine two surface integrals that are needed for the derivation of the forms of the Coulomb gauge potentials expressed in terms of the fields used in [12]. It is possible to express the well-known expression for the scalar potential [2] in the form…”

“…No assumption is made about the equations that generate the field. This method had been used to construct electromagnetic potentials of relevance to the Aharonov-Bohm effect [12]. The two approaches have been compared by Woodside [14].…”