Explicitly integrable models of quantum field theory with exponential interaction in two-dimensional space

Explicit expressions are obtained for the Heisenberg operators of the two-dimensional models of quantum field theory described by the system of equations $\square u_\alpha=g\exp(ku)_\alpha$ as functionals of asymptotic fields $\varphi_\alpha^\mathrm{in}$ satisfying the equations $\square\varphi_\alpha^\mathrm{in}=0$ and appropriate commutation relations. It is shown that in the presence of a finite-dimensional internal symmetry group, when $k$ is the Caftan matrix of a semisimple Lie group, the perturbation series for the operators $\exp(-u_\alpha)$ degenerate into polynomials in the coupling constant $g$, the degrees of the polynomials being related to the structure of the fundamental representations of the corresponding group.