Stochasticity, topology, and spin

Complex Schroedinger equation is transformed to spinor or coupled scalar field equations replacing the imaginary unit $i$ by a matrix $\begin{bmatrix} 0 & 1 \-1 & 0 \end{bmatrix}$. New perspecive on stochasic approach is developed with spin as topological invariant and mass having stochastic origin in this Spinor Random Field formalism.