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-Buttiker 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.
Henrik Bruus, MIC - Dept of Micro- and Nanotechnology, Technical University of Denmark Karsten Flensberg, Oersted Laboratory, Niels Bohr Institute, Denmark
1. First and second quantization ; 2. The electron gas ; 3. Phonons: coupling to electrons ; 4. Mean field theory ; 5. Time evolution pictures ; 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. Imaginary time 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. 1D electron gases and Luttinger liquids ; A. Fourier transformations ; B. Exercises ; C. Index