Variational approach to the QCD wave functional: Dynamical mass generation and confinement

We perform a variational calculation in the SU(N) Yang-Mills theory in 3+1 dimensions. Our trial variational states are explicitly gauge invariant, and reduce to simple Gaussian states in the zero coupling limit. Our main result is that the energy is minimized for the value of the variational parameter away from the perturbative value. The best variational state is therefore characterized by a dynamically generated mass scale M. This scale is related to the perturbative scale ΛQCD by the relation αQCD(M)=({π}/4)N. Taking the one-loop QCD {β} function and ΛQCD=150 MeV we find (for N=3) the vacuum condensate ({α}/{π})〈F²〉=0.008 GeV⁴.