Diagrammatics: Lectures On Selected Problems In Condensed Matter TheoryThe introduction of quantum field theory methods has led to a kind of “revolution” in condensed matter theory. This resulted in the increased importance of Feynman diagrams or diagram technique. It has now become imperative for professionals in condensed matter theory to have a thorough knowledge of this method.There are many good books that cover the general aspects of diagrammatic methods. At the same time, there has been a rising need for books that describe calculations and methodical “know how” of specific problems for beginners in graduate and postgraduate courses. This unique collection of lectures addresses this need.The aim of these lectures is to demonstrate the application of the diagram technique to different problems of condensed matter theory. Some of these problems are not “finally” solved. But the development of results from any section of this book may serve as a starting point for a serious theoretical study. |
Contents
| 1 | |
2 ElectronElectron Interaction | 17 |
3 ElectronPhonon Interaction | 71 |
4 Electrons in Disordered Systems | 101 |
5 Superconductivity | 177 |
6 Electronic Instabilities and Phase Transitions | 241 |
Appendix A Fermi Surface as Topological Object | 333 |
Appendix B Electron in a Random Field and Feynman Path Integrals | 339 |
Bibliography | 345 |
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Common terms and phrases
2p F Abrikosov A.A. analytic continuation anomalous approximation averaged BCS theory behavior calculations coefficient conductivity consider contribution Cooper pairs correlation corresponding Coulomb defined density determined diagram technique diagrammatic diagrams shown dielectric dielectric permeability disorder dºp Dyson equation Dzyaloshinskii I.E. 1963 electron-phonon interaction electronic lines energy expression Fermi level Fermi point Fermi surface Fermi-liquid Fermion Feynman finite fluctuations Fourier free electron frequency Gorkov L.P. Green's function Green’s imaginary impurities instability integral interaction lines introduced lattice limit magnetic Matsubara metal momenta momentum N(EF normal obtain one-dimensional order parameter particle perturbation phonon polarization operator pole potential pseudogap quantum quasiparticles random field renormalization result Sadovskii M.V. scattering self-energy shown in Fig ſº spectrum spin summation superconductor take into account temperature theory Tºo vector vertex vertex correction Ward identity write zero