Resolution of the Hierarchy of Many-Body Green's Functions

Abstract

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)→∞, \(\varOmega\)(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.