= Covariance of a field equation does not fix homogeneous solutions
If a <differential operator> $L$ is a <linear map> and has nonzero <kernel of a linear map>, the equation $LA=J$ determines $A$ only up to a <homogeneous solution>. <Lorentz covariance> of $L$ and $J$ therefore does not force independently selected solutions in different <inertial frames> to obey a particular <tensor> transformation law. A covariant <Green function> and consistently transformed homogeneous data do provide such a choice. For the <four-potential> in <Lorenz gauge>, $\Box A^\mu=-\mu_0J^\mu$ still permits $A^\mu\mapsto A^\mu+\partial^\mu\chi$ with $\Box\chi=0$, a <residual Lorenz gauge symmetry>. Constant spatial potentials for zero sources are a concrete example.
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