Seminarium KMMF "Teoria Dwoistości"

In the first part I will review Bogoliubov theory for many-body quantum systems, in particular its relation to quadratic Hamiltonians and Hartree-Fock theory of the electron gas. Moreover I will discuss the approximate transmutation of fermions into bosons (in dimension d > 1 !) through introduction of collective modes and present post-Hartree-Fock energy corrections obtained by this approach.In the second part I will discuss in more detail the specific implementation of a Fermi-Bose transmutation used to proof the mentioned energy corrections and comment on more recent results, in particular concerning the time evolution of a Fermi gas.