A relation between the coupling constants of interacting nonlinear scalar field ~(Xo, xl ) and a spinor one ~(Xo, Xl ), Lin t = -g 2 /2 e 2~ -g' e e ~ was established. This relation leads to the finite series of perturbation theory for the dynamical variable e -~. In the classical limit ~ -+ 0 the considered system turns out to be described by the supersymmetric Liouville equation.
A presence of the internal symmetry Lie-B/tcklund group for some classical models of field theory is known to be the reason for their exact integrability in two-dimensional space-time [1]. The well-known examples with the Boze fields make it clear that this property conserves in the quantum region as well. The condition of exact integrability is formulated via the same terms of group representation theory as in the classical region. The proportionality of the matrix of coupling constants to the Cartan matrix of some simple Lie algebra is the condition of finiteness of the perturbation theory series for definite dynamical variables of the systems with expotential interactions both in the classical and the quantum case [2]. One may expect, therefore, that the internal symmetry group ~ conserve in the quantum case, though at present we cannot explicitly describe it.