Quadratic actions, semi-classical approximation, and delta sequences in Gaussian analysis

A mathematically rigorous realization of Feynman integrals is given. The construction works for quadratic actions (there is only a restriction to limited time intervals). These techniques enable the calculation of the semi-classical approximation for a given Feynman propagator. Finally, delta sequences in Gaussian analysis are presented and their connection to semi-classical approximation is discussed.