Renormalization of Hartree-Fock-Bogoliubov Equations

Hartree-Fock-Bogoliubov (HFB) equations are the most sophisicated mean-field approach to decribe pairing correlations in various systems, such as nuclei, neutron stars and ultracold dilute Fermi atom gases. It is natural to apply zero-range approximation to the paring force in these systems. However, the solutions to HFB equations diverge with zero-range approximation. This book systemically present the techique to cure the divergence. In this book, this local pairing treatment is also applied to vortices in neutron matter and in cold atom gas with a large scattering length, where it is shown that there is a matter depletion at the core area of a vortex state, which can be interpreted as a bosonic feature of such systems. This book is of interest to graduate students in condensed matter physics and nuclear physics.