the absence of a mass pole in the vacuum Green’s function of a colored object implies that the object is repelled by the vacuum, and hence attracted to other colored objects to form a color singlet by virtue of the interaction with the vacuum. An illustration of this mechanism is afforded through the use of a simple model[@gluon; @GSM] of the gluon two-point function given by $$D\left( (P-K)^2\right) = \frac{3\eta ^2\pi ^4}{g^2}\delta
^{(4)}(P-K).\label{3.1}$$ At the present level of approximation, the self-energy dressing from the vacuum is provided by the equations (\[2.2\]) and (\[2.3\]). The solutions to these implied by (\[3.1\]) are $$\begin{aligned}
A(P^{2}) & = & \left\{
\begin{array}{cl}
2, & P^{2}\leq \frac{\eta ^{2}}{4} \\
\frac{1}{2}\left[ 1+\left(1+\frac{2\eta ^{2}}{P^{2}}\right)
^{\frac{1}{2}}\right] , & P^{2}\geq \frac{\eta ^{2}}{4}
\end{array}\right. \nonumber \\ & &  \nonumber \\
B(P^{2}) & = & \left\{
\begin{array}{cl}
(\eta ^{2}-4P^{2})^{\frac{1}{2}}, &
\; \; \; \; \; \; \; \; \; \; \; \; P^{2}\leq \frac{\eta ^{2}}{4} \\
0, & \; \; \; \; \; \; \; \; \; \; \; \; P^{2}\geq \frac{\eta ^{2}}{4}
\end{array}\right. . \label{3.2}\end{aligned}$$ That the solutions (\[3.2\]) produce a model of confinement as described above can be seen by the absence of a solution to the expression $P^2+M^2(P^2)=0$, 