Lattice gauge theory calculations in 1 + 1 dimensions and the approach to the continuum limit

Abstract

Lattice perturbation theory for gauge theories of strong interactions is studied for (1 + 1)-dimensional Abelian gauge theories. Strong-coupling expansions for the theory's mass spectrum are carried out to order $\frac{1}{{g}^{16}{a}^{16}}$ ($a=\mathrm{lattice}\mathrm{spacing}$). These expansions are extrapolated to the continuum limit using Pad\'e approximants. These high-order results are compared to $\frac{1}{{g}^{8}{a}^{8}}$ expansions reported previously, and convergence to known continuum theory results is noted. In many cases, agreement between the lattice calculations and continuum theory results exists to 2-3%. These calculational methods generalize to (3 + 1)-dimensional theories.