Green function of Quantum Liouville Problem via Exact Summation of perturbation series

Abstract

The path integral treatment of the Quantum Liouville Problem based on exact summation of the Feynman perturbation series is presented in its original form. Using Fourier transform on the end point, we have established a recurrence equation between successive terms of the perturbation series. This leads us to sum up exactly all the terms and deduce the Green function of the problem.