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

Abstract

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 form 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 ${\Lambda }_{QCD}$ by the following relation: ${\alpha }_{QCD}(M)=\frac{\pi }{4}\frac{1}{N}$. Taking the one loop QCD $\beta$- function and ${\Lambda }_{QCD}=150Mev$ we find (for N=3) the vacuum condensate $\frac{\alpha }{\pi }<F^2>=0.008Ge{v}^4$.

37 pages, (1 Figure available upon request), preprint LA-UR-94-2727, PUPT-1492

References in corpus (1)

• Hadron Masses from the Valence Approximation to Lattice QCD

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