description of confinement in fact relies on the interaction between dressed quarks diminishing at separations beyond the characteristic length scale, $R_0$, at which point the quark Green’s function approaches its vacuum value. The quarks are then repelled by the vacuum due to absence of a mass pole in the vacuum quark Green’s function. The effective “rising potential" of traditional models of confinement occurs here as a result of the repulsive interaction of quarks with the vacuum in combination with the decreasing interaction between dressed quarks with increasing separation. Such a description has proven successful in the formulation of a confining nontopological soliton model for baryons[@GSM]. This mechanism arises naturally here, and is pursued as a possible realization of confinement.

The paper is organized as follows. In Sec.2 the general features of the QPV are given along with the reduction of Eq.(\[IBS\]) to a form suitable for computer applications. The solution of the homogeneous Bethe-Salpeter equation (\[BS\]) is also discussed there. In Sec.3 a discussion of confinement is presented in the context of a particular model which yields analytic solutions to both the inhomogeneous Bethe-Salpeter and Schwinger-Dyson equations (\[IBS\]) and (\[SDE\]) respectively. Also discussed there is the criteria for the formation 