Role of the non-locality of the vector potential in the Aharonov-Bohm effect

TL;DR

This paper explores how the non-local nature of electromagnetic potentials in Coulomb gauge influences the Aharonov-Bohm effect, explaining how distant fields affect electron interference patterns without direct contact.

Contribution

It provides a detailed analysis of the non-locality of vector potentials and its role in the Aharonov-Bohm effect, clarifying a fundamental quantum phenomenon.

Findings

Non-local potentials depend on fields at all points in space.

The Aharonov-Bohm effect arises from the non-locality of potentials.

Fields outside the electron's path influence interference patterns.

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 at first instance responsible for the puzzle associated with the Aharonov-Bohm effect: that its interference pattern is affected by fields in a region of space that the electron beam never enters.