| his thesis is divided into two parts. The first describes a study of the dilute Fermi gas with short range repulsive interactions in 2D, with special emphasis on questions related to the validity of Fermi liquid theory. We find that despite the existence of non-perturbative effects due to two-dimensionality, namely linearly dispersing excitations of "bound" holes, the system remains in a Fermi liquid state. The quasi-particles are both long lived and weakly interacting. We also provide a microscopic calculation of the Fermi liquid parameters which determine the response functions in the standard way.;The second part describes an investigation into the crossover from cooperative Cooper pairing to independent bound state formation and condensation in a system of fermions with attractive interactions in 3D. We employ a functional integral framework which reproduces the BCS theory in weak coupling and the theory of the dilute Bose gas in strong coupling (for temperatures below a very large dissociation scale). Our analysis includes a calculation of the crossover between these two limits in... |
