Algebraic and Diagrammatic Methods in Many-Fermion Theory

The importance of electron correlation effects to the accurate description of the electronic structure of atoms, molecules, and crystals is now widely recognized. In this text, modern theories and methods of incorporating electron correlation contributions are developed using a diagrammatic and algebraic formulation. The goal is the elucidation of modern theories of electronic structure within a common language to facilitate an understanding of the interconnections between the approaches. As a further aid to this understanding, the methods developed in the text are illustrated with example systems from molecular and solid state quantum mechanics. The techniques presented here for the education of graduate students in physical chemistry and physics treat as operator algebra, Hartree-Fock methods, Feynman diagrams, configuration interaction, many-body perturbation theory and the coupled cluster method.