Green’s Functions and Feynman Diagrams
In the preceding chapters we studied how the various linear responses of a metal are modified by the effect of the interaction between electrons, and then, how the electron-phonon interaction together with the electron-electron interaction modify the phonon properties and the electronic properties, particularly, the magnetic ones in a metal. In those discussions we used the equation of motion approach with the mean field approximation in dealing with the interaction effects. In this chapter we introduce the method of Green’s functions and Feynman diagrams which is indispensable in further pursuing those problems, as will be illustrated in the succeeding chapters. As for the method of Green’s functions and Feynman diagrams there are a number of excellent references. See, for instance, Refs. [1.2–1.6, 7.9, 8.1–8.7]. The purpose of this chapter is to present a simple introduction so as to enable those readers who are not familiar with this method to proceed to the succeeding chapters.
KeywordsFeynman Diagram Thermodynamic Potential External Line Dyson Equation Electron Line
Unable to display preview. Download preview PDF.
- 8.1L. P. Kadanoff and G. Baym, Quantum Statistical Mechanics ( Addison-Wesley, Redwood City, 1989 ).Google Scholar
- 8.2A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Prentice Hall, Englewood Cliff., N. J., 1963 ).Google Scholar
- 8.3R. Abe, Statistical Mechanics, transi. Y. Takahashi ( Univ. of Tokyo Press, Tokyo, 1975 ).Google Scholar
- 8.4G. Rickayzen, Green’s Functions and Condensed Matter ( Academc Press, London, 1980 ).Google Scholar
- 8.5J.-P. Blaizot and G. Ripka, Quantum Theory of Finite Systems ( MIT Press, Cambridge, 1986 ).Google Scholar