Fermion stochastic calculus in Dirac-Fock space
David Applebaum · Journal of Physics A Mathematical and General · 1995
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.