Path integral of topological defects in superfluids and superconductors

In the first part of the thesis the student will study the finite-temperature path integral approach to superfluids and superconductors by analyzing different models involving bosons and fermions: Gross-Pitaevskii, Ginzburg-Landau and Bardeen-Cooper-Schrieffer. In the second part the student will investigate the formalism (not yet fully developed) which enables one to microscopically introduce topological defects (quantized vortices and dark solitons) in the models of superfluids and superconductors. In the third part of the thesis the student will derive the superfluid density and the critical temperature of the superfluid-normal phase transition in the framework of the Kosterlitz-Thouless proliferation of topological defects in systems with reduced spatial dimensionality.