Many-Particle Theory,

The quantum theory of many-particle systems has applications in various branches of physics including condensed matter, atomic, molecular, nuclear and high-energy. An understanding of this theory is therefore important to most students of physics and Many-Particle Theory is an excellent introduction to the subject. Many-Particle Theory presents a detailed and logical account of the theory and techniques used. Basic subjects such as Green's functions and Feynman diagrams are discussed in detail, and many examples and applications are given, such as the Hartee-Fock approximation, superconductivity and the Kondo problem. Due to the detailed derivations and the fact that only a grasp of basic quantum mechanics is assumed, the book is an ideal textbook for graduate students and teachers of physics. The comprehensive bibliography contains many recent books and articles for further studies. Many-Particle Theory is a translation of the second German edition, which is an expanded version of the popular first edition. All three authors, E K U Gross, E Runge and O Heinonen, are well respected researchers in the field.

Table of Contents:
Fundamentals and examples: Systems of identical particles. Second quantization for fermions. Second quantization for bosons. Unitary transformations and field operators. Example: the Hamiltonian of translationally invariant systems in second quantization. Density operators. The Hartree-Fock approximation. Restricted Hartree-Fock approximation and the symmetry dilemma. Hartree-Fock for translationally invariant systems. The homogeneous electron gas in the Hartree-Fock approximation. Long-range correlations in the electron-gas: plasmons. Phonons. Superconductivity. Green's functions: Pictures. The single-particle Green's function. The polarization propagator, the two-particle Green's function, and the hierarchy of equations of motion. Perturbation theory: Time-independent perturbation theory. Time-dependent perturbation theory and adiabatic turning-on of the interaction. Particle and hole operators and Wick's theorem. Feynman diagrams. Diagrammatic calculation of the vacuum amplitude. An example: the Gell-Mann-Brueckner correlation energy of a dense electron gas. Diagrammatic calculation of the single-particle Green's function: Dyson's equation. Diagrammatic analysis of the Green's function G(k, w). Self-consistent perturbation theory, an advanced perspective on Hartree-Fock theory. The quasi-particle concept. Diagrammatic calculation of the two-particle Green's function and the polarization propagator. Effective interaction and dressed vertices, an advanced perspectives on plasmons. Perturbation theory at finite temperatures. Fermi liquid theory: Introduction. Equilibrium properties. Transport equation and collective modes. Microscopic derivation of the Landau Fermi liquid theory. Application to the Kondo problem.