  The use of internal variables for the description of relativistic particles
with arbitrary mass and spin in terms of scalar functions is reviewed and
applied to the stochastic phase space formulation of quantum mechanics.
Following Bacry and Kihlberg a four-dimensional internal spin space $\bar S$ is
chosen possessing an invariant measure and being able to represent integer as
well as half integer spins. $\bar S$ is a homogeneous space of the group $SL(2,
C)$ parametrized in terms of spinors $\a\in C_2$ and their complex conjugates
$\bar\a$. The generalized scalar quantum mechanical wave functions may be
reduced to yield irreducible components of definite physical mass and spin
$[m,s]$, with $m\ge 0$ and $s=0, 1/2, 1, 3/2 ...$, with spin described in terms
of the usual $(2s+1)$-component fields. Viewed from the internal space
description of spin this reduction amounts to a restriction of the variable
$\a$ to a compact subspace of $\bar S$, i.e. a ``spin shell'' $S^2_{r=2s}$ of
radius $r=2s$ in $ C_2$. This formulation of single particles or single
antiparticles of type $[m,s]$ is then used to study the geometro- stochastic
(i.e. quantum) propagation of amplitudes for arbitrary spin on a curved
background space-time possessing a metric and axial vector torsion treated as
external fields. A Poincar\'e gauge covariant path integral-like representation
for the probability amplitude (generalized wave function) of a particle with
arbitrary spin is derived satisfying a second order wave equation on the
Hilbert bundle constructed over curved space-time. The implications for the
stochastic nature of polarization effects in the presence of gravitation are
pointed out and the extension to Fock bundles of bosonic and fermionic type is
briefly mentioned.
