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Topics and Methods in Condensed Matter Theory
From Basic Quantum Mechanics to the Frontiers of Research
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. .
I-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.