A quantum stochastic calculus for fermions is developed where the basic integrators are based on Dirac fields and the charge operator. The associated Ito formula has seven non-trivial correction terms. Conditions are found for the solutions of stochastic differential equations to be unitary and it is shown that the corresponding quantum stochastic flow manifests a broken symmetry whereby the particle and antiparticle noises no longer balance each other. An abstract theory of such flows is then developed. By employing the unification between boson and fermion stochastic calculi, we are able to develop the entire theory using boson Fock spaces.
Using the techniques of quantum stochastic calculus the author constructs dilations of the Bloch equations into boson and fermion 'noise baths'. Relaxation times and equilibrium values are computed in terms of the stochastic coupling parameters at different temperatures. The most general dilation of the standard form of the equations into a combination of boson and fermion noise is described using classical Brownian motion, the Clifford process and boson and fermion annihilation and creation processes. The author extends the scheme to take account of Poisson processes.