What is the relativistic generalization of a linearly rising potential?

Recent progress in summing graphs of non-Abelian gauge theories focuses attention on certain manifestly Lorentz-invariant classical action-at-a-distance theories, whose solution allows for the construction of field-theoretic Green functions in the WKB approximation. The sum of graphs is of QED type, except that the gluon propagator is modified to incorporate the renormalization-group-invariant charge $\text{g}\text{(k)}$. The purely phenomenological choice $\text{g}{}^2\text{～ k}{}^{\mathrm{?2}}$ is equivalent non-relativistically to a linearly rising potential and yields a fully relativistic classical action-at-a-distance theory with exactly soluble circular orbits, whose Bohr quantization yields an asymptotic approximation to the poles of the Green function. One finds asymptotically linear Regge trajectories, but other phenomenological aspects are not as promising when only a linearly rising potential is used (in common with other phenomenological studies). As a redeeming feature, there do not appear to be any obvious pathologies of the sort familiar from string theories and ad hoc generalizations of linearly rising potentials.