Lorenz gauge condition

The Lorenz gauge condition requires the four-divergence of the electromagnetic four-potential to vanish. It makes Maxwell’s equations for the potentials take wave-equation form while leaving residual gauge freedom.

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Electromagnetic four-potential: A four-vector potential whose derivatives determine the electric and magnetic fields. Its four-divergence is the quantity constrained to zero.
Special relativity: A theory of space and time in which physical laws are invariant across inertial frames. The condition is naturally expressed using relativistic four-vectors.
Ludvig Lorenz: A Danish physicist who developed a retarded-potential formulation of electrodynamics in the nineteenth century. The gauge condition is named for this physicist, not Hendrik Lorentz.
Coulomb gauge: An electromagnetic gauge condition requiring the spatial divergence of the vector potential to vanish. Unlike the Lorenz condition, it singles out a spatial frame and makes the scalar potential instantaneous.
Maxwell's equations: Four equations describing how electric and magnetic fields arise and evolve. Applying the condition turns the potential equations into wave equations.
Four-vector: A quantity with four components that transforms as a vector under Lorentz transformations. The four-potential’s components combine into a relativistic object.
Retarded potential: A field potential evaluated at the earlier time when its source could influence the observation point. Lorenz’s formulation used retarded potentials and the condition now bearing his name.
Temporal gauge: An electromagnetic gauge choice in which the scalar potential is set to zero. It fixes a different feature of the potentials and does not impose vanishing four-divergence.
Gauge transformation: A change in electromagnetic potentials that leaves the observable electric and magnetic fields unchanged. Residual transformations preserve the Lorenz condition when their gauge function satisfies a wave equation.
Electromagnetic potential: Scalar and vector potentials from which electric and magnetic fields can be calculated. The Lorenz condition constrains the relativistic combination of these potentials.