Cini M. Topics and Methods in Condensed Matter Theory: From Basic Quantum Mechanics to the Frontiers of Research

Springer, 2007. — 440 p. — SBN-13 9783540707264.Темы и методы теории конденсированного состояния: от фундаментальной квантовой механики до границ исследований
This book provides material for courses in theoretical physics for undergraduate and graduate students specializing in condensed matter, including experimentalists who want a thorough theoretical background; the advanced part should be of interest to research workers too. A good first course in quantum mechanics is assumed. Here a variety of many-body phenomena in condensed matter are discussed, with special attention paid to the understanding of strong correlation effects. This requires a variety of theoretical tools (diagram expansions, groups, recursion methods and more). The text, which arose naturally from teaching, is eminently readable and the mathematical treatments are explained in enough detail to be followed easily. Proofs of all the relevant theorems are provided, but the main emphasis is always on the physical meaning or applicability of the results. Many examples are provided for illustration and also serve as worked problems.Introductory Many-Body Physics
Basic Many-Body Quantum Mechanics
Adiabatic Switching and Time-Ordered series
Atomic Shells and Multiplets
Green’s Functions as Thought Experiments
Hopping Electron Models: an Appetizer
Many-body Effects in Electron Spectroscopies
Symmetry in Quantum Physics
Group Representations for Physicists
Simpler Uses of Group Theory
Product of Representations and Further Physical Applications
More on Green Function Techniques
Equations of Motion and Further Developments
Feynman Diagrams for Condensed Matter Physics
Many-Body Effects and Further Theory
Non-Equilibrium Theory
Non-Perturbative Approaches and Applications
Some Recursion Techniques with Applications
Aspects of Nonlinear Optics and Many-Photon Effects
Selected Exact Results in Many-Body Problems
Quantum Phases
Pairing from repulsive interactions
Algebraic Methods
Appendices
Appendix 1: Zero-point Energy in a Pillbox
Appendix II-Character Tables
Proof of the Wigner-Eckart Theorem