Exact propagator of a two dimensional system

Abstract

The propagator for an electron moving in a two-dimensional system under the influence of a transverse magnetic field B, a time varying external force field f(s) and a nonlocal harmonic force, is

evaluated exactly by using Feynman's path integrals method. The actual problem is transformed into the one of an electron moving in the magnetic fields under the external force fields and the local harmonic force by using Stratonovich's transformation. The classical action of the transformed problem is evaluated by using 2 x 2 matrix introduced by Papadopoulos in the calculation of the magnetization of the harmonically bounded charges. The propagator of the original problem is

obtained by taking the gaussian average of the electron propagator in transformed problem.