Direct, analytic solution for the electromagnetic vector potential in any gauge

TL;DR

This paper presents an exact analytic solution for the electromagnetic vector potential in any gauge derived directly from Maxwell's equations, including both gauge-invariant and gauge-dependent components, without imposing a gauge condition.

Contribution

It introduces a gauge-independent analytic solution for the vector potential applicable in any gauge, derived directly from Maxwell's equations without gauge constraints.

Findings

Solution includes gauge-invariant and gauge-dependent parts

Applicable to arbitrary time-dependent charge-current distributions

No gauge condition needed in the derivation

Abstract

We derive an analytic solution for the electromagnetic vector potential in any gauge directly from Maxwell's equations for potentials for an arbitrary time-dependent charge-current distribution. No gauge condition is used in the derivation. Our solution for the vector potential has a gauge-invariant part and a gauge-dependent part. The gauge-dependent part is related to the scalar potential.