Relativistic many-body theory. A new field-theoretical approach.
type: Item
instance of: scholarly article
title: Relativistic many-body theory. A new field-theoretical approach.
zbMATH Open document ID: 1218.81003
DOI: 10.1007/978-1-4419-8309-1
author: Ingvar Lindgren
published in: Springer Series on Atomic, Optical, and Plasma Physics
publication date: 2011-03-31T00:00:00Z
review text: 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.
reviewed by: Gert Roepstorff
Mathematics Subject Classification ID: 81-02
Mathematics Subject Classification ID: 81V45
Mathematics Subject Classification ID: 81V70
Mathematics Subject Classification ID: 81U20
Mathematics Subject Classification ID: 81Q40
zbMATH DE Number: 5872983
zbMATH Keywords: many-body theory
zbMATH Keywords: atomic physics
zbMATH Keywords: many-electron system
zbMATH Keywords: perturbation theory
zbMATH Keywords: relativistic theory
zbMATH Keywords: QED effects
zbMATH Keywords: Green's functions
zbMATH Keywords: S-matrix
zbMATH Keywords: Bethe-Salpeter equation
zbMATH Keywords: numerical calculations
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-1-4419-8309-1
OpenAlex ID: W2483768090
description: scientific article; zbMATH DE number 5872983