  We develop a many-particle quantum-hydrodynamical model of fermion matter
interacting with the external classical electromagnetic and
gravitational/inertial and torsion fields. The consistent hydrodynamical
formulation is constructed for the many-particle quantum system of Dirac
fermions on the basis of the nonrelativistic Pauli-like equation obtained via
the Foldy-Wouthuysen transformation. With the help of the Madelung
decomposition approach, the explicit relations between the microscopic and
macroscopic fluid variables are derived. The closed system of equations of
quantum hydrodynamics encompasses the continuity equation, and the dynamical
equations of the momentum balance and the spin density evolution. The possible
experimental manifestations of the torsion in the dynamics of spin waves is
discussed.
