The hydrodynamic model including the spin degree of freedom and the electromagnetic field is discussed. In this derivation, we apply electromagnetism for a macroscopic medium proposed by Minkowski. For the equation of motion of spin, we assume that the hydrodynamic representation of the Pauli equation is reproduced when the many-body effect is neglected. Then the spin-magnetic interaction in the Pauli equation is converted to a part of the magnetization. The fluid and spin stress tensors induced by the many-body effect are obtained by employing the algebraic positivity of the entropy production in the framework of the linear irreversible thermodynamics, including the mixing effect of the irreversible currents. We further construct the constitutive equation of the polarization and the magnetization. Our polarization equation is more reasonable compared to another result obtained using electromagnetism for a macroscopic medium proposed by de Groot-Mazur.

• Received 18 November 2012

DOI:https://doi.org/10.1103/PhysRevC.87.034902