Calculation of the superpropagators of massive particles in nonpolynomial quantum field theories

A method of constructing the superpropagators of massive particles, i.e. the Fouries transforms of the two point Green's functions $F(x)=\sum_{n=1}^\infty c(n)[\lambda\Delta_F(x)]^n$ in the quantum field theories with nonpolynomial Lagrangians is proposed. The method is based on applying definite differential operators in the coupling constant $\lambda$ to the simplest superpropagator for which the modified perturbation theory expansion in the powers of $\lambda$ and $\ln\lambda$ is found.