ABSTRACT
The integrals in the path integral are strongly oscillating and can only be defined by analytic continuation. It is important to note that the continuous expression is just a notation for the discrete version of the path integral, but formal manipulations will be much easier to perform in this continuous formulation. Furthermore, the integral is only defined through the analytic continuation in time. As long as the Hamiltonian is quadratic in the momenta, the stationary phase approximation for the momentum integral is exact. In practical situations one splits from the action the quadratic part in the coordinates and velocities and considers the rest as a perturbation.
