Abstract
Lattice gauge theories in two dimensions are studied with regard to investigating the continuum limit. The effective interaction is calculated for the lattice gauge theories for QED [U(1)] and $\mathrm{SU}(N)$ to all orders in the gauge coupling and is shown to reproduce the usual Schwinger and 't Hooft models, respectively, in the limit of zero lattice spacing. However, lattice gauge theories in strong coupling have, in general, qualitatively different $S$ matrices than their expected continuum analogs. Except for the $\mathrm{SU}(N)$ lattice gauge theory in the formal limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$, ${g}^{2}N$ fixed, the lattice introduces additional four-or-more-body forces which are not present in the continuum.
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