  We generalize the methods used in the theory of correlation dynamics and
establish a set of equations of motion for many-body correlation green's
functions in the non-relativistic case. These non-linear and coupled equations
of motion describe the dynamical evolution of correlation green's functions of
different order and transparently show how many-body correlations are generated
by the different interaction terms in a genuine nonperturbative framework. The
nonperturbative results of the conventional green's function theory are
included in the present formalism as two limiting cases (the so-called ladder
diagram summation and ring diagram summation) as well as the familiar
correlation dynamics of density-matrices in the equal time limit. We present
explicit expressions for three- and four-body correlation functions that can be
used to dynamically restore the trace relations for spin-symmetric fermi
systems and study numerically the relative importance of two-, three- and
four-body correlations for nuclear configurations close to the groundstate.
