Maxwell equations with spin density

Abstract

According to the Maxwell equations in its standard form the sources of the magnetic field are electric currents. But modern physics has discovered that another source of the magnetic field of, say, ferromagnets is the spin of unpaired electrons. This source can be described by a spin density σ (r, t) that should appear in Maxwell’s equations. One reason why this is usually avoided may be that the spin contribution can be simulated by a suitable current density j(r, t). However, this simulation is only a mathematical manipulation without a physical basis since the origin of an electron spin cannot be understood in terms of the classical picture of rotating electrons considered charged spheres. Therefore we think that it is more appropriate to directly include the spin density as a source in Maxwell’s equations.