Velocity operator approach to a Fermion system

In this paper, we formulate a velocity operator approach to a three-dimensional (3D) Fermion system. Following Sunakawa, introducing density and velocity operators, we treat 3D quantum fluid dynamics in the system. We get a collective Hamiltonian in terms of collective variables. The lowest order collective Hamiltonian is diagonalized. This diagonalization leads us to a Bogoliubov transformation for Boson-like operators.