New approach to perturbation theory of many-particle systems

We derive an infinite hierarchy of integral equations 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 0 Green function is given. A new self-consistent equation for the k = 0 Green function is solved to yield the well-known self-energy relation ₁₁ – ₀₂ = which plays the role of a self-consistency condition on the theory.