Randomness in the Quantum Description of Neutral Spin 1/2 Particles

Recently the path integral quantization of the classical spin model was accomplished by Nielsen and Rohrlich. The configuration space of classical spin is the unit sphere with punctures at poles. Motivated by the fact that the Nelson's stochastic mechanics idea was to randomize the configuration space variable of the classical system, we give a review of the probabilistic approaches to the quantization of spin 1/2, with emphasis on the Dankel's problem of finding the probabilistic description of the Pauli equation in terms of stochastic diffusion processes. The original Dankel's analysis referred to the rigid top, and the problem of the point particle limit was left unsolved. Our observation is that if the spin stochastic process refers to the unit sphere with punctures, then Dankel's results provide a solution to the Pauli equation with no need of extra limiting procedures. The effects of the magnetic field can be successfully incorporated into the formalism.