AN INTRODUCTORY GUIDE TO GREEN’S FUNCTION METHODS IN NUCLEAR MANY-BODY PROBLEMS

We present an elementary and fairly detailed review of several Green’s function methods for treating nuclear and other many-body systems. We first treat the single-particle Green’s function, by way of which some details concerning linked diagram expansion, rules for evaluating Green’s function diagrams and solution of the Dyson’s integral equation for Green’s function are exhibited. The particle-particle hole-hole (pphh) Green’s function is then considered, and a specific time-blocking technique is discussed. This technique enables us to have a one-frequency Dyson’s equation for the pphh and similarly for other Green’s functions, thus considerably facilitating their calculation. A third type of Green’s function considered is the particle-hole Green’s function. RPA and high order RPA are treated, along with examples for setting up particle-hole RPA equations. A general method for deriving a model-space Dyson’s equation for Green’s functions is discussed. We also discuss a method for determining the normalization of Green’s function transition amplitudes based on its vertex function. Some applications of Green’s function methods to nuclear structure and recent deep inelastic lepton-nucleus scattering are addressed.

FEYNMAN DIAGRAM EXPANSION IN THE BALANCE-EQUATION TRANSPORT THEORY

In the balance-equation theory for hot-electron transport, the fact that electrons and phonons have different temperatures in the initial density matrix prevents one from directly invoking the conventional statistical Wick theorem to carry out a high-order perturbation analysis. Nevertheless, the well-known Feynman rules and diagram technique are demonstrated to be applicable to any order of the electron—impurity and electron—phonon interactions within the Keldysh Green’s function formalism of this theory.