## Covariant Isolation from an Abelian Gauge Field of Its Nondynamical Potential, Which, When Fed Back, Can Transform Into a "Confining Yukawa"

**Authors:** Steven Kenneth Kauffmann

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 Maxwellequation
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.

**Comments:** 12 pages, Also archived as arXiv:1005.1101 [physics.gen-ph]

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### Submission history

[v1] 11 May 2010

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