Perturbation Theory in Path Integral Formalism

This lecture covers perturbation theory in the path integral formalism, focusing on Feynman diagrams and the perturbative expansion of the free energy of an anharmonic oscillator. The instructor discusses connected and disconnected diagrams, the replica trick, and the scaling of diagrams with the number of copies. The lecture also delves into the semi-classical approximation, explaining how classical particle motion emerges when the particle's wavelength is much smaller than the potential's characteristic length scale. The instructor provides insights into the relationship between perturbation theory and the semi-classical approximation, emphasizing their distinct applications in solving non-exactly soluble systems.