A set of differo-integral equations for many-body connected temperature Green's functions is established which is non-perturbative in nature and provides a reasonable truncation scheme with respect to the order of many-body correlations.The method can be applied to nuclear systems at finite temperature.
Despite its centrality in the mathematical structure of perturbative many-body theory, the total Green's function for the many-body time-dependent Schrodinger equation has been ignored for decades, superseded by single-particle Green's functions, for which a vast portion of the literature has been devoted. In this paper, we give the first computation the total Green's function for the time-dependent Schrodinger equation for a non-interacting system of identical particles, setting the stage for a fresh interpretation of perturbative many-body physics.
(by translator) A perturbation theory is developed for normal many-particle systems by expanding the inverse of the advanced and retarded Green functions. Both systems with direct interactions and systems with interactions through a quantum field are considered. For the former, the infinite set of coupled equations is written down and the various methods of decoupling discussed. Systems with weak, hard sphere type, or coulomb interactions are considered and the connections with other methods discussed. For systems with quantum field interactions, the chain of equations involves both fermion and boson Green functions and the first approximation can be much better than in earlier cases. This latter approach seems to be more convenient when collective oscillations are important.