Fondements mathématiques des intégrales de chemin Feynman path integrals

Abstract

In this thesis we are interest in the formalism of the Feynman path integral and we present it in its theoretical aspect. We have introduced it in three approaches, which are essential in the most applications, Feynman path integral diagram, Trotter formula and Perturbation series. We have tried to avoid its initial aspect, the physics, and to use it with the mathematical arguments. We applied this formalism for a non relativistic problem, Schrodinger equation for the Morse potential, as well as relativistic problems, free Feschbach-Villars equation and Klein-Gordon equation.