Abstract
The time-dependent Hartree-Fock theory is generalized in order to include two-body collisions. Using a method similar to the projection method of quantum statistics an exact and closed equation is derived for the one-particle density matrix which takes into account both the mean field and the two-body residual interactions. In the limit of long mean free path of the particles, the exact equation for the one-particle density matrix is simplified by introducing some general statistical properties of the residual interactions. An equation is obtained for the expectation values of operators which includes both the mean-field contributions and the correlations due to the residual interactions. The effects of the correlations on the fluctuations of collective variables are discussed. It is shown that the statistical approximations introduced do not destroy the energy and the momentum conservations.
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