In electromagnetism, the Lorenz gauge condition or Lorenz gauge, for Ludvig Lorenz, is a partial gauge fixing of the electromagnetic vector potential by requiring The name is frequently confused with Hendrik Lorentz, who has given his name to many concepts in this field. The condition is Lorentz invariant. The condition does not completely determine the gauge: one can still make a gauge transformation where is the four-gradient and is a harmonic scalar function (that is, a scalar function satisfying the equation of a massless scalar field). The Lorenz condition is used to eliminate the redundant spin-0 component in the representation theory of the Lorentz group. It is equally used for massive spin-1 fields where the concept of gauge transformations does not apply at all. Description In electromagnetism, the Lorenz condition is generally used in calculations of time-dependent electromagnetic fields through retarded potentials. The condition is where is the four-potential, the comma denotes a partial differentiation and the repeated index indicates that the Einstein summation convention is being used. The condition has the advantage of being Lorentz invariant. It still leaves substantial gauge degrees of freedom. In ordinary vector notation and SI units, the condition is where is the magnetic vector potential and is the electric potential; see also gauge fixing. In Gaussian units the condition is A quick justification of the Lorenz gauge can be found using Maxwell's equations and the relation between the magnetic vector potential and the magnetic field: Therefore, Since the curl is zero, that means there is a scalar function such that This gives the well known equation for the electric field, This result can be plugged into the Ampère–Maxwell equation, This leaves, To have Lorentz invariance, the time derivatives and spatial derivatives must be treated equally (i.e. of the same order). Therefore, it is convenient to choose the Lorenz gauge condition, which gives the result A similar procedure with a focus on the electric scalar potential and making the same gauge choice will yield These are simpler and more symmetric forms of the inhomogeneous Maxwell's equations. Note that the Coulomb gauge also fixes the problem of Lorentz invariance, but leaves a coupling term with first-order derivatives. Here is the vacuum velocity of light, and is the d'Alembertian operator. These equations are not only valid under vacuum conditions, but also in polarized media, if and are source density and circulation density, respectively, of the electromagnetic induction