RESOLUTION OF HIERARCHY OF MANY-BODY GREENS FUNCTIONS

The rigorous evolution equations for the one-body Green's functions (g>, g<) describing an imperfect gas in a finite volume are not closed (an analogue of B–B–G–K–Y hierarchy for the many-body distribution functions). The analysis of these equations are made in terms of proper connected diagrams. It is shown that in the bulk limit: N (particle number)→∞, ΩΩ(volume)→∞ such that N/Ω=constant, these equations can be reduced to the closed equations, which are however, non-linear and non-Markoffian, in contrast to the original hierarchy equations. © 1969, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.