Many-Body Methods for Atoms, Molecules and Clusters

I. Many-Electron Systems and the Electron Propagator 1. Systems of identical particles 2. Second quantization 3. One-particle Green's function II. Formalism of Diagrammatic Perturbation Theory 4. Perturbation theory for the electron propagator 5. Introducing diagrams 6. Feynman diagrams 7. Time-ordered or Goldstone diagrams III. Approximations and Computational Schemes 8. Self-energy and the Dyson equation 9. Algebraic-diagrammatic construction (ADC) 10. Direct ADC procedure for the electron propagator 11. Intermediate-state representation (ISR) 12. Order relations and separability IV. N-Electron Excitations 13. Polarization propagator 14. ADC and ISR approaches to the polarization propagator 15. Random-phase approximation (RPA) V. A Look at Related Methods 16. Algebraic propagator methods 17. Coupled-cluster methods for generalized excitations Appendix A1 Basic tools A2 Proof of the Gell-Mann and Low theorem A3 Proof of Wick's theorem A4 Time-ordered diagrams: derivation of Goldstone rules A5 Dyson expansion method for the static self-energy part A6 Proofs of order relations A7 Linear response theory and the polarization propagator A8 Superoperator approach to the electron propagator A9 Compilation of ADC expressions