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Abstract
Approximate solutions for the ground state of QCD are obtained in both the continuum and lattice formulations of the theory. The solution in the continuum case is obtained by constructing gauge-invariant trial wavefunctionals, and regulating ultraviolet divergences in the Schrodinger wavefunctional equation. Remarkably, this state seems to be dominated at large scales by multimonopole configurations, as originally suggested by 't Hooft and Mandelstam. In the lattice formulation, a method is developed for systematically exponentiating infinite series of vacuum diagrams in strong-coupling lattice SU(N) gauge theory. The result is a lattice ground state containing new information about large scale vacuum fluctuations, and which has the same long-wavelength structure as the continuum solution. The method itself is an efficient alternative to the standard Kogut-Susskind perturbative expansion, and avoids the use of group integrations. It seems possible to extend this method to non-perturbative lattice calculations in the intermediate coupling regime.
