  New collective coordinates, related to the field at the `center' of the
monopoles, are proposed. A systematic computation of the infrared properties of
2+1- and 3+1- dimensional Yang-Mills theory is now possible and is related to
solutions of classical equations with constraints at isolated points. For
2+1-dimensional Yang-Mills theory, monopoles of a specific size proportional to
$g^{-2}$ dominate and a semiclassical technique is applicable. For
3+1-dimensional Yang-Mills theory, the formalism incorporates a monopole
condensate naturally, and is therefore a correct starting point for
computations of confinement properties. The method also provides a precise way
of going beyond the dilute gas approximation for instantons in 3+1-dimensions.
Another algorithm, which uses only the quadratic form of the action and
corrections via renormalized perturbation theory, is proposed as a viable
scheme of computation for all length scales.
