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For Abelian gauge theory a properly relativistic gauge is developed bysupplementing the Lorentz condition with causal determination of the timecomponent of the four-vector potential by retarded Coulomb transformation ofthe charge density. This causal Lorentz gauge agrees with the Coulomb gauge forstatic charge densities, but allows the four-vector potential to have alongitudinal component that is determined by the time derivative of thefour-vector potential's time component. Just as in Coulomb gauge, the twotransverse components of the four-vector potential are its sole dynamical part.The four-vector potential in this gauge covariantly separates into a dynamicaltransverse four-vector potential and a nondynamical timelike/longitudinalfour-vector potential, where each of these two satisfies the Lorentz condition.In fact, analogous partition of the conserved four-current shows each tosatisfy a Lorentz-condition Maxwell equation system with its own conservedfour-current. Because of this complete separation, either of these four-vectorpotentials can be tinkered with without affecting its counterpart. Since itsatisfies the Lorentz condition, the nondynamical four-vector potential times aconstant with dimension of inverse length squared is itself a conservedfour-current, and so can be fed back into its own source current, whichtransforms its time component into an extended Yukawa, with both exponentiallydecaying and exponentially growing components. The latter might be themechanism of quark-gluon confinement: in non-Abelian color gauge theory theYukawa mixture ratio ought to be tied to color, with palpable consequences for"colorful" hot quark-gluon plasmas.

Covariant isolation from an Abelian gauge field of its nondynamical potential, which, when fed back, can transform into a "confining Yukawa"