ABSTRACT
This chapter deals for the most part with a systematic microscopic description of equilibrium weakly interacting Bose gas (WIBG) in one, two, and three dimensions. Our analysis is based on Beliaev’s diagrammatic technique [1] for Matsubara Green’s functions, regularized with small but finite Bogoliubov’s symmetrybreaking terms. This approach was discussed in detail in Reference [2]; the analytic part of this chapter is based on that paper. At the end of the chapter, we will present the mean-field theory for weakly interacting Fermi gas, or the Bardeen-Cooper-Schrieffer (BCS) solution.
