Nonperturbative confinement in quantum chromodynamics. II. Mandelstam’s gluon propagator

Abstract

It is shown that Mandelstam’s approximate equation for the gluon propagator has a solution with very singular infrared behavior. At the origin in the squared momentum variable there are a double pole, a branch-point, and an accumulation of complex first-sheet branch-points. Although the double pole is suggestive of confinement, the existence of acausal complex singularities indicates a deficiency in this first step of the approximation scheme.