The Kirchhoff gauge

Abstract

We discuss the Kirchhoff gauge in classical electrodynamics. In this gauge the scalar potential satisfies an elliptical equation and the vector potential satisfies a wave equation with a nonlocal source. We find the solutions of both equations and show that, despite of the unphysical character of the scalar potential, the electric and magnetic fields obtained from the scalar and vector potentials are given by their well-known retarded expressions. We note that the Kirchhoff gauge pertains to the class of gauges known as the velocity gauge.

12 pages

References in corpus (4)

• Historical roots of gauge invariance
• From Lorenz to Coulomb and other explicit gauge transformations
• Is the Lorentz signature of the metric of spacetime electromagnetic in origin?
• Instantaneous fields in classical electrodynamics

Cited by in corpus (6)

• How potentials in different gauges yield the same retarded electric and magnetic fields
• Comment on 'A generalized Helmholtz theorem for time-varying vector fields by A. M. Davis, [Am. J. Phys. 74, 72-76 (2006)]'
• On Feynman's handwritten notes on electromagnetism and the idea of introducing potentials before fields
• How to obtain the covariant form of Maxwell's equations from the continuity equation
• Can the Lorenz-gauge potentials be considered physical quantities?
• The Coulomb static gauge