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Lecture Notes by Prof. Helmut Eschrig
TOC
1 The Solid as a Quantum Many-Body System
1.1 The Coulomb Hamiltonian of the Solid
1.2 Reduced Density Matrices and Densities
1.3 Correlation Functions
2 Green’s Functions
2.1 Spectral Representation
2.2 Equation of Motion
2.3 Complex Time
2.4 The Interaction Picture
2.5 Wick’s Theorem
2.6 Feynman Diagrams
2.7 The Self-Energy
2.8 Thermodynamic Quantities
3 Green’s Functions in the Superconducting State
3.1 The Bogoliubov-Valatin Transformation
3.2 The Nambu Structure
3.3 Green’s Functions and Vertices for the Electron-Nucleon System
4 Split-off of High-Energy Parts
4.1 Classification of Primary Diagrams
4.2 Migdal’s Theorem
4.3 Leading Order Self-Energies
5 The Low Energy Equations
5.1 The Quasi-Particle Renormalization
5.2 The Electron-Phonon Self-Energy
5.3 The Electron-Electron Self-Energy
5.4 Bloch Function Representation on the Fermi Surface
6 Strong Coupling Theory of the Transition Temperature
6.1 Linearization of Eliashberg’s Equations
6.2 The Tc Formula
6.3 The Dirty Limit
6.4 The Cut-Off Frequency
7 Physical Properties of the Superconducting State
7.1 Eliashberg’s Non-Linear Equations
7.2 The Quasiparticle Density of States
7.3 The Thermodynamic Critical Field
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