  The problem of fermion dynamics is studied using the Q-function for fermions.
This is a probabilistic phase-space representation, which we express using
Majorana operators, so that the phase-space variable is a real antisymmetric
matrix. We consider a general interaction Hamiltonian with four Majorana
operators and arbitrary properties. Our model includes the Majorana Hubbard and
Fermi Hubbard Hamiltonians, as well as general quantum field theories of
interacting fermions. Using the Majorana Q-function we derive a generalized
Fokker-Planck equation, with results for the drift and diffusion terms. The
diffusion term is proved to be traceless, which gives a dynamical
interpretation as a forwards-backwards stochastic process. This approach leads
to a model of quantum measurement in terms of an ontology with real vacuum
fluctuations.
