Correlation Dynamics of Green's Functions

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.