New Cluster Expansion Method in Lattice Gauge Theory

Abstract

2) have been reported by many authors, and their results are very successful and give us values of various physical quantities such as the string tension and the mass gap. However, they are no more than numerical experiments. To understand the theory, we should have an explicit analytic expressions of these physical quantities. One method to get an analytic expression of them is the strong coupling expansion (S.C.E.).3) This expansion gives us a qualitative understanding of the lattice gauge theory. Especially the quark confinement and existence of the mass gap in the strong coupling limit are manifest in this expansion. The expansion series are convergent in the strong coupling region,4) and agreement between the Monte Carlo measurement and the strong coupling expansion series is very good in this region. But the series do not appear to be convergent in the weak coupling region, which we are interested in. Expansion parameter fl (inverse coupling constant squared) or u(fl) (coefficient of the fundamental representation in the character expansion of the Boltzmann factor exp(flS» used in this expansion is large or nearly equal to 1, respectively, in the