Path integral theory of interacting fermionic many-body systems: towards a semiclassical approximation

Abstract

This master thesis works towards expressing the dynamics of an interacting fermionic system on a lattice using the bosons that carry their interaction, with the long-term goal of developping a semiclassical theory for fermions. After some refreshers on many-body quantum systems and classical Lagrangian mechanics, Feynman's path integral is introduced and particularized to the coherent state representation. The remaining part of the master thesis is devoted to the exposition and application of a method to achieve the goal mentioned above. Using the path integral to a mixed Hamiltonian describing fermions interacting with each other by boson exchange, it is first shown that we recover an interacting fermionic system when the bosons are eliminated. Then, the elimination of the fermions from the mixed system is performed and discussed.