Transversally confined, noncausal gluons

A nonperturbative approach to the gluonic sector of four-dimensional QCD is defined, in which a gap equation is used to generate a mass scale $M$ dimensional transmutation in an arbitrary axial gauge, using a modification of Halpern's method of replacing conventional functional integration over gauge potentials by integration over equivalent field strengths. A consistency condition is used to show that, without further radiative corrections, the gluonic QCD system is apparently diaelectromagnetic against the insertion of color-electromagnetic fields when the spatial shape of the nonperturbative vacuum state is associated with tubes of color-electric or -magnetic flux. A final Gaussian approximation to the relevant functional integral over field strength leads to an extremely simple result of "effective gluons" propagating as "free particles" with a matrix-valued mass term, by means of a noncausal "propagator" that is effectively confined to the interior of a spatial tube, and that falls off with a large momentum ${\left[k^2\right]}^{-2\mathrm{}}$ as ${\left[k^2\right]}^{-2\mathrm{}}$. A non-Gaussian extension of this result for the effective gluon propagator (EGP) can be guessed. Either from of EGP may be used to compute a finite, gauge-invariant condensate $〈g^2{F}^2〉$ which corresponds to color-electric flux inside and color-magnetic flux outside the tube, or vice versa. The introduction of quarks leads to a "modified QED" in an external, tadpole-generated field, where the EGP replaces the bare photon propagator.