  We formulate a microscopic theory of the decay of a compound nucleus through
fission which generalizes earlier microscopic approaches of fission dynamics
performed in the framework of the adiabatic hypothesis. It is based on the
constrained Hartree-Fock-Bogoliubov procedure and the Generator Coordinate
Method, and requires an effective nucleon-nucleon interaction as the only input
quantity. The basic assumption is that the slow evolution of the nuclear shape
must be treated explicitely, whereas the rapidly time-dependent intrinsic
excitations can be treated by statistical approximations. More precisely, we
introduce a reference density which represents the slow evolution of the
nuclear shape by a reduced density matrix and the state of intrinsic
excitations by a canonical distribution at each given shape of the nucleus. The
shape of the nuclear density distribution is described by parameters
("generator coordinates"), not by "superabundant" degrees of freedom introduced
in addition to the complete set of nucleonic degrees of freedom. We first
derive a rigorous equation of motion for the reference density and,
subsequently, simplify this equation on the basis of the Markov approximation.
The temperature which appears in the canonical distribution is determined by
the requirement that, at each time t, the reference density should correctly
reproduce the mean excitation energy at given values of the shape parameters.
The resulting equation for the "local" temperature must be solved together with
the equations of motion obtained for the reduced density matrix.
