Many-Body Quantum Theory in Condensed Matter Physics

This book is an introduction to the techniques of many-body quantum theory with a large number of applications to condensed matter physics. The basic idea of the book is to provide a self-contained formulation of the theoretical framework without losing mathematical rigor, while at the same time providing physical motivation and examples. The examples are taken from applications in electron systems and transport theory.

On the formal side, the book covers an introduction to second quantization, many-body Green’s function, finite temperature Feynman diagrams and bosonization. The applications include traditional transport theory in bulk as well as mesoscopic systems, where both the Landau-Büttiker formalism and recent developments in correlated transport phenomena in mesoscopic systems and nano-structures are covered. Other topics include interacting electron gases, plasmons, electron-phonon interactions, superconductivity and a final chapter on one-dimensional systems where a detailed treatment of Luttinger liquid theory and bosonization techniques is given.

Having grown out of a set of lecture notes, and containing many pedagogical exercises, this book is designed as a textbook for an advanced undergraduate or graduate course, and is also well suited for self-study.

Table of Contents

1: FIRST AND SECOND QUANTIZATION

2: THE ELECTRON GAS

3: PHONONS; COUPLING TO ELECTRONS

4: MEAN-FIELD THEORY

5: TIME DEPENDENCE IN QUANTUM THEORY

6: LINEAR RESPONSE THEORY

7: TRANSPORT IN MESOSCOPIC SYSTEMS

8: GREEN’S FUNCTIONS

9: EQUATION OF MOTION THEORY

10: TRANSPORT IN INTERACTING MESOSCOPIC SYSTEMS

11: I MAGI NARY-Tl ME GREEN’S FUNCTIONS

12: FEYNMAN DIAGRAMS AND EXTERNAL POTENTIALS

13: FEYNMAN DIAGRAMS AND PAIR INTERACTIONS

14: THE INTERACTING ELECTRON GAS

15: FERMI LIQUID THEORY

16: IMPURITY SCATTERING AND CONDUCTIVITY

17: GREEN’S FUNCTIONS AND PHONONS

18: SUPERCONDUCTIVITY

19: 1 D ELECTRON GASES AND LUTTINGER LIQUIDS

APPENDIX A: FOURIER TRANSFORMATIONS