Lorenz gauge condition

In electromagnetism, the Lorenz gauge condition or Lorenz gauge (after Ludvig Lorenz) is a partial gauge fixing of the electromagnetic vector potential by requiring ${\displaystyle \partial _{\mu }A^{\mu }=0.}$ The name is frequently confused with Hendrik Lorentz, who has given his name to many concepts in this field.^[1] The condition is Lorentz invariant. The Lorenz gauge condition does not completely determine the gauge: one can still make a gauge transformation ${\displaystyle A^{\mu }\mapsto A^{\mu }+\partial ^{\mu }f,}$ where ${\displaystyle \partial ^{\mu }}$ is the four-gradient and ${\displaystyle f}$ is any harmonic scalar function: that is, a scalar function obeying ${\displaystyle \partial _{\mu }\partial ^{\mu }f=0,}$ the equation of a massless scalar field.

The Lorenz gauge condition is used to eliminate the redundant spin-0 component in Maxwell's equations when these are used to describe a massless spin-1 quantum field. It is also used for massive spin-1 fields where the concept of gauge transformations does not apply at all.