Quantum Hydrodynamics of Spinning Particles in Electromagnetic and Torsion Fields

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