The particle spectra of confining field theories - Kenway, R; Richard D. Kenway (1978)
﻿ Massive QED (Schwinger model) for one and two fermion species in 1+1 dimensions is studied using Hamiltonian lattice techniques. Bound-state masses are calculated as strong-coupling expansions in inverse powers of the dimensionless coupling constant. Various Pade approximant methods for extracting continuum predictions from these are compared. The non-relativistic limit of both lattice theories is the lattice linear potential model. This can be solved exactly. It is used to test convergence of the sequence of Pade approximants. The investigation is continued for the ordinary Schwinger model. At all coupling strengths, the best continuum estimates for bound-state masses come from values of the Pade approximants at non-zero lattice spacing. Two different lattice formulations of the two-species Schwinger model are studied. Both have a restoration of chiral SU(2) symmetry as the fermion mass vanishes. The corresponding symmetric vacuum is too complicated to do a perturbative calculation beyond second order, where the low-lying states are those of a Heisenberg antiferromagnetic chain, in qualitative agreement with the continuum theory. Strong-coupling expansions are carried out to high orders about the unsymmetric vacua of the massive theories. Continuum estimates for bound-state masses are compared. For weak coupling their convergence is understood in terms of the linear potential model. But for strong coupling convergence is slow; neither lattice can account for the whole particle spectrum, though each treats part of it well. Matrix methods are studied in an attempt to obtain better convergence from low-order calculations. Strong-coupling expansions for the Hamiltonian matrix in a non-degenerate subspace are extrapolated to zero lattice spacing using matrix Pade approximants. Improved continuum estimates ore obtained from the scalar mass matrix of the ordinary Schwinger model, but not from the pseudoscalar mass matrix.