Spin Densities in Pseudo - Classical Kinetic Theory

It is shown that classical many-particle systems based on N=1 supersymmetry allow for observable consequences of the spin degrees of freedom. In contrast to the one-particle system, where a consistent formulation of spinspace density is impossible, the many-particle system allows for spin to enter into the equations of motion in a non-trivial way. This density can then be directly compared to the decomposition of the Wigner-operator in terms of spin matrices. We discuss the quantization of a classical kinetic theory for N=1 particles, both in the non-relativistic and the relativistic context. From an expansion of the Dirac-spinors in terms of large and small components it is seen that in the non-relativistic limit the pseudo-scalar, the time-like component of the axial-vector current and the spatial components of the vector-current vanish. The spatial components of the axial vector-current vanish in the classical limit. The classical appearance of spin is due to the spin-tensor contribution.