Color confinement and the quantum-chromodynamic vacuum. III

In earlier papers it was shown that if soft gluons do not propagate in the vacuum state the vacuum expectation value of the modified Coulomb interaction develops a singularity at zero momentum that leads to the confinement of color. The consistency of this picture is established with the demonstration that if the interaction is singular soft gluons do not propagate. This conclusion is shown to be independent of most approximations. Taken together the three papers in the series provide a framework for calculating the most important aspects of color confinement in quantum chromodynamics.