Computing Feynman path integrals in real time

We review the algorithm of Feit, Fleck and Steiger as a method to calculate Feynman path integrals in real time under very general circumstances ranging from the simple potential problems for the Schroedinger equation to cases involving time dependent perturbations, resonances and coupling to a white noise source. Dirac equation can be studied with minor modifications. We test the algorithm in the one-dimensional Dirac equation using the potential tanh (λχ) which allows for an exact solution. (orig.)