New approach to perturbation theory of many-particle systems

An infinite hierarchy of integral equations is derived for the Green functions of a many-particle system. This set of equations forms the basis of a unified approach to the perturbation theory of many boson and many fermion systems and avoids the introduction of the adiabatic hypothesis. It is demonstrated how a well-known ground state perturbation theory of a system of interacting fermions is obtained without introducing disconnected diagrams. It is shown that the formalism allows a self-consistent determination of the condensate Green function of a condensed Bose system and a derivation of the Beliaev, Hugenholtz, and Pines result for the single-particle k not= O Green function is given. A new self-consistent equation for the K = O Green function is solved to yield the well-known self-energy relation Σ11-Σ02=μ which plays the role of a self-consistency condition on the theory. (author)