An Implicit Gauge Condition for Auxiliary Potentials in Inhomogeneous Media

Auxiliary potentials are indispensable mathematical tools in classical electromagnetic theory and other branches of physics. The curl of the electric and magnetic vector potentials is defined through relationships to field variables; this is ambiguous because the curl is unchanged by adding the gradient of an arbitrary scalar potential. These redundant degrees of freedom are eliminated through gauge fixing, wherein a relationship between the vector potential's divergence and the scalar potential is specified. Explicitly, defining this relationship leads to difficulties in inhomogeneous media. This communication presents an implicit gauge that avoids these difficulties and generalizes the Lorenz gauge to inhomogeneous propagation media.