On the Nonlocaity in the Goulomb Gauge External Field Problem

TL;DR

This paper explores the apparent nonlocality in the Coulomb gauge external field problem in electrodynamics, providing a local explanation and deriving the Aharonov-Bohm effect using gauge-invariant field strengths.

Contribution

It offers a local interpretation of nonlocal effects in Coulomb gauge and presents a gauge-invariant decomposition of the Lorentz-force, deriving the Aharonov-Bohm effect from field strengths.

Findings

Illustrates nonlocality with a specific example

Provides a local explanation for nonlocal behavior

Derives Aharonov-Bohm effect using field strengths

Abstract

The apparent nonlocality of the Coulomb gauge external field problem in electrodynamics is illustrated with an example in which nonlocality is especially striking. Explanation of this apparent nonlocal behaviour based on a purely local picture is given. A gauge invariant decomposition of the Lorentz-force into two terms with clear physical meanings is pointed out. Based on this decomposition derivation of the Aharonov-Bohm effect in terms of field strengths alone is given.