Covariant Isolation from an Abelian Gauge Field of Its Nondynamical Potential, Which, When Fed Back, Can Transform into a “Confining Yukawa”

Abstract

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 fourcurrent. 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.