Green's function theory of one and many particle systems-1〜3-

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.

Clasine van Winter

Hannes Bolterauer

Tomokazu Kato, Tetsuro Kobayashi, Mikio Namiki

The formal theory of Green functions is reviewed for many particle problems in nuclear physics or in solid state physics. In particular, one- and two-particle Green functions are discussed in detail. The Feynman amplitudes are also explained together with the effective potential and its applications. This article contains the following sections: §1. Preliminary remarks §2. Definition of Green functions §3. Structure of equations satisfied by Green functions 3.1 One-particle Green function 3.2 Two-particle Green function §4. Perturbation theory and its foundation §5. Spectral representation and its application §6. Connection with reaction matrix §7. Amplitudes and their matrix 7.1 Definitions of amplitudes and effective potential 7.2 Nuclear optical model 7.3 One electron in insulators and semi-conductors Appendix I. Functional differentiation Appendix II. Schwinger's dynamical principle Appendix III. Polaron problem

L. Ya. Kobelev

A. A. Katanin

We consider formulations of the functional renormalization-group (fRG) flow for correlated electronic systems with the dynamical mean-field theory as a starting point. We classify the corresponding renormalization-group schemes into those neglecting one-particle irreducible six-point vertices (with respect to the local Green’s functions) and neglecting one-particle reducible six-point vertices. The former class is represented by the recently introduced DMF 2 RG approach [31], but also by the scale-dependent generalization of the one-particle irreducible representation (with respect to local Green’s functions, 1PI-LGF) of the generating functional [20]. The second class is represented by the fRG flow within the dual fermion approach [16, 32]. We compare formulations of the fRG approach in each of these cases and suggest their further application to study 2D systems within the Hubbard model.