Operator Products in the SU($\mathrm{\infty }$) Principal Chiral Model

The SU($N$) principal chiral model is asymptotically free and integrable in $1+1$ dimensions. In the large-$N$ limit, there is no scattering, but correlation functions are {\em not} those of a free field theory. We briefly review the derivation of form factors for local operators. Two-point functions for such operators are known exactly. The two-point function of scaling-field operators has the short-distance behavior expected from the renormalization group. We briefly discuss non-vacuum operator products. The ultimate goal is to derive the Lagrangian field theory from this axiomatic quantum-field-theory formalism.