Quark confinement and vortices in massive gauge-invariant QCD

Massive gauge-invariant QCD can support vortices (analogous to Nielsen-Olesen strings) of nearly finite classical action per unit area (there is a logarithmic short-distance singularity which is of little consequence). These vortices lead, in analogy to Abelian lattice-gauge theories, to confinement of fractionally charged quarks and color screening for gluons. In this paper, we make some qualitative remarks about the (Minkowski-space) dynamics which follows from this sort of confinement, studying not only $\text{q}\text{q}$ processes but also qqq processes. For the latter, the effective long-range vortex-induced interaction is approximately described as a sum of two-body potentials each of half the strength of the $\text{q}\text{q}$ potential (just as for the asymptotically free short-distance potentials), and linearly rising non-relativistically. There is an essential two-dimensionality about the confinement process which suppresses what would be the transverse degrees of freedom of strings joining quarks. A fully relativistic dynamics is given which is amenable to a simple phenomenological joining of long- and short-distance effects, with a running coupling constant such that g²(k) ～ k^?2 for small k. Spin-dependent potentials have no linearly-rising parts, and there are no strong Van der Waals forces. Little is said about gluon dynamics, except to point out the existence of rather massive hadronic glueballs and of (classically singular) instanton-like solutions which are screened at large distances.