  The modified Navier-Stokes equation describing the velocity field in the
superfluid quantum space is loaded by the external Lorentz force introducing
electromagnetic fields. In order to open the path for getting the
\Schrodinger-Pauli equation describing the behavior of a particle with spin-1/2
in the magnetic field we need to extend the continuity equation to take into
account conservation of spin flows on the 3D sphere. This extension includes
conservation of the density distribution function in 6D space, that is a
multiplication of the 3D Euclidean space by the 3D sphere of unit radius. The
special unitary group SU(2) underlies the rotations of the spin on this sphere.
This group is isomorphic to the group of quaternions containing the real 4x4
matrices of norm 1. Transition to the quaternion group opens up the way to the
possibility of describing the spin-1/2 behavior in a magnetic field as a motion
of a spin flag on the 2D sphere. Maxwell's electromagnetic field theory
manifests itself in the quaternion group basis by the natural manner.
