GENERAL NONPERTURBATIVE MASS GAP TO FIRST-ORDER IN 1/V

Abstract

The cluster expansion of the Lanczos matrix is studied in both vacuum and non-vacuum sectors of Hilbert space. The first order analytic diagonalization of the expanded Lanczos matrix is employed to obtain an expression for the lowest energy state in a given sector. Subtraction of the vacuum energy at the same order gives a non-perturbative expression for the lowest mass gap of that sector to order 1 V. This general result is applied to the axial and tensor glueball sectors of SU(3) lattice gauge theory and the ratio R = MA MT is calculated analytically. We find that this approximate for R agrees with the higher order t expansion computations up to the transition from strong to weak coupling ..