  A Gaussian operator representation for the many body density matrix of
fermionic systems, developed by Corney and Drummond [Phys. Rev. Lett, v93,
260401 (2004)], is used to derive approximate decoupling schemes for their
dynamics. In this approach the reduced single electron density matrix elements
serve as stochastic variables which satisfy an exact Fokker-Planck equation.
The number of variables scales as ~N^2 rather than ~exp(N) with the basis set
size, and the time dependent Hartree Fock approximation (TDHF) is recovered in
the "classical" limit. An approximate closed set of equations of motion for the
one and two-particle reduced density matrices, provides a direct generalization
of the TDHF.
