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

The cluster expansion of the Lanczos matrix is studied in both vacuum and non-vacuum sectors of Hilbert space. The first order analytic diag onalization of the expanded Lanczos matrix is employed to obtain an ex pression for the lowest energy state in a given sector. Subtraction of the vacuum energy at the same order gives a non-perturbative expressi on for the lowest mass gap of that sector to order 1/V. This general r esult is applied to the axial and tensor glueball sectors of SU(3) lat tice gauge theory and the ratio R = M(A)/M(T) is calculated analytical ly. We find that this approximate for R agrees with the higher order t expansion computations up to the transition from strong to weak coupl ing at 2/g(2) similar to 1.5, thus explicitly demonstrating the non-pe rturbative nature of the mass-gap expression.