Formal Theory of Green Functions

Abstract

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