Quantum hydrodynamics of spinning particles in electromagnetic and torsion fields

TL;DR

This paper develops a quantum hydrodynamical model for fermion matter interacting with electromagnetic, gravitational, inertial, and torsion fields, linking microscopic quantum behavior to macroscopic fluid dynamics.

Contribution

It introduces a consistent hydrodynamical formulation for Dirac fermions in external fields, incorporating torsion effects into quantum fluid equations.

Findings

Derived explicit relations between microscopic and macroscopic variables.

Formulated a closed system of quantum hydrodynamics equations.

Discussed potential experimental signatures of torsion in spin wave dynamics.

Abstract

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.