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