Generalized green functions

Lorenz S. Cederbaum

The theory of Green's functions is briefly reviewed. It is discussed which properties of a quantum system and which physical processes can be described by Green's functions. A general approximation scheme to evaluate Green's functions and propagators is presented. Particular attention is paid to the one-particle Green's function and to the particle–particle propagator which is a relevant component of the two-particle Green's function. Several illustrative applications are presented and related to experiment.

Jaime Merino, A. Levy Yeyati

S. Y. Tsay Tzeng, T.T.S. Kuo, Yiharn Tzeng +2 more

In conventional Green's function methods the vertex function \ensuremath{\Gamma} is generally energy dependent. However, a model-space Green's function method where the vertex function is manifestly energy independent can be formulated using energy-independent effective interaction theories based on folded diagrams and/or similarity transformations. This is discussed in general and then illustrated for a 1p1h model-space Green's function applied to a solvable Lipkin many-fermion model. The poles of the conventional Green's function are obtained by solving a self-consistent Dyson equation and model space calculations may lead to unphysical poles. For the energy-independent model-space Green's function only the physical poles of the model problem are reproduced and are in satisfactory agreement with the exact excitation energies. \textcopyright{} 1996 The American Physical Society.

B. Frank, L. A. Murray

A general formalism is developed for the treatment of cumulant Green functions related to the Ising model problem. Within this formalism, Green-function equations of motion and spectral theorems are given. The need for cumbersome transformations between ordinary and cumulant quantities is thereby eliminated. A general expression for the cumulant Green function in terms of semi-invariant thermal averages is also derived. The relation of the formalism to certain decoupling schemes is made.

F. Beck, Benno Fuchssteiner