The supersymmetric Liouville equation in the quantum region

Abstract

A relation between the coupling constants of interacting nonlinear scalar field ϕ(x0, x1) and a spinor one \(\psi (x_{\text{o}} ,x_1 ),L_{\operatorname{int} } = - \bar g^2 /2e^{2\phi } g\prime e^\phi \bar \psi \psi \) was established. This relation leads to the finite series of perturbation theory for the dynamical variable e -ϕ . In the classical limit ħ→0 the considered system turns out to be described by the supersymmetric Liouville equation.