What distinguishes topologically trivial from non-trivial superfluids
in interacting many-body systems with a conserved number of particles?
What is the meaning and fate of Majorana zero-energy modes in
interacting fermionic superfluids? These are questions that require a
concrete operational answer if one seriously considers using these
physical systems for quantum information processing purposes. Most of
what we know about topological superfluids and Majorana excitations is
based on a mean-field approximation, the Bogoliubov-de Gennes
approach, that breaks particle-number conservation and, by
construction, displays a particle-hole symmetry and thus a zero mode
structure. I will attempt to answer the questions above from both
basic physics principles, and concrete models perspectives.