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

2025/07/02 by Yang, Kuo-Ho, Nevels, Robert D.
#Classical Physics (physics.class-ph) #FOS: Physical sciences

paper · doi:10.48550/arxiv.2507.02104

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.

Citations

• Velocity, temporal and generalized Kirchhoff gauges
• Note on the transformation from the Lorenz gauge to the Coulomb gauge
• Velocity Gauge Potentials in Electrodynamics
• Potentials of a uniformly moving point charge in the Coulomb gauge

Related

• The Nature of the Vector and Scalar Potentials and Gauge Invariance in the Context of Gauge Theory
• Derivation and physical interpretation of the general solutions to the wave equations for electromagnetic potentials
• Vector Potential Electromagnetic Theory with Generalized Gauge for Inhomogeneous Anisotropic Media
• On some properties of the electromagnetic field and its interaction with a charged particle
• Vector potentials in gauge theories in flat spacetime