The vector potential in any gauge is expressed as the retarded potential plus a gradient built from the scalar potential, which reduces to the known gauge transformation from the Lorenz gauge.
Velocity Gauge Potentials in Electrodynamics
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abstract
Vector and scalar potentials are used for convenience in solving boundary value problems involving electromagnetic (EM) fields. The potentials are made unique by choosing a non-unique gauge relationship. The most commonly used gauges are those named for Lorenz and Coulomb, both of which may be defined as special cases of what is termed the velocity gauge, or v-gauge. This generalized gauge is not usually taught to students of electrodynamics. In this paper, we review properties of the velocity gauge, including EM field invariance, and demonstrate its application via an example.
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Direct, analytic solution for the electromagnetic vector potential in any gauge
The vector potential in any gauge is expressed as the retarded potential plus a gradient built from the scalar potential, which reduces to the known gauge transformation from the Lorenz gauge.