Relativistic many-body theory. A new field-theoretical approach.
In 1986 the second edition of the book [Atomic many-body theory. Berlin: Springer (1986)] written by \textit{I. Lindgren} and \textit{J. Morrison} appeared. At that time, it was an up-to-date presentation of basic ideas, non-relativistic structures, and fascinating results in the treatment of atomic systems. The entire treatment was based on the Schrödinger equation with the Coulomb interaction, a scheme that started with work by Slater, Hartree, Fock, and others. Since then there has been a tremendous conceptual development in the theory of many-body systems which now includes QED effects, the use of advanced mathematical methods such as relativistic quantum field theory, Green's functions, the covariant evolution operator formalism, and the scattering matrix. The proper relativistic theory uses the Dirac equation for electrons and the Bethe-Salpeter equation for the bound-state problem. The present book aims to provide an overview and to summarize the results obtained with the modern formalism, but is still largely based on the previous book with Morrison. Thus, the reader is assumed to be familiar with its content. The main text of the present book has three parts. Part I provides details of the basic formalism regarding the many-body perturbation theory. Part II describes various numerical procedures for calculating QED effects on bound states of electrons, i.e., the S-matrix method, the Green's-function method, and the covariant evolution operator method. Part III combines QED with the many-body perturbation theory. All methods are illustrated using numerical examples. This textbook is a reliable guide for advanced graduate students and researchers.
scientific article; zbMATH DE number 5872983