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.
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Atkinson et al. (1982) studied this question.