Bernstein processes and spin-1/2 particles

A pure jump Bernstein process whose probability density is the product of the solution of the (imaginary time) Schrödinger equation and its adjoint equation, associated to a class of time dependent Hamiltonians describing spin-1/2 particles, is constructed. A path integral representation of these solutions, in terms of this process, is obtained as well as a calculus over path space for the associated Euclidean quantum observables.