Systematic technique for computing infrared properties of 2+1- and 3+1- dimensional Yang-Mills theory

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.