Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

The Many-body Problem

David Pines

Published Jan 21, 1971• 571 citations
OpenAlex

Abstract

Editors ForewordA Survey, with Emphasis on Physical ConsiderationsMathematical Principles and TechniquesSpecific ProblemsPapers for Supplemental ReadingReprints (various papers (1953-1960) on the following subjects:General FormulationElectron GasInteracting Fermion SystemInteracting Boson SystemsSuperconductivity

Related papers

Introductory Chapter: Statistical and Theoretical Considerations on Magnetism in Many-Body Systems

Sergio Curilef

IntechOpen eBooks•Oct 28, 2020•1 citation

Selected Theoretical Comparisons for Bosons

Nick P. Proukakis, Matthew J. Davis, S. A. Gardiner

One of the aims of the organisers of the FINESS conferences, and of the editors of this book, has been to encourage dialogue between researchers working in the general area of non-equilibrium superfluids. The researchers come from widely different backgrounds, and come with a broad array of favourite theoretical techniques. In this chapter we present an incomplete survey of figures from previously published papers that make a comparison between selected subsets of different theoretical methods. The goal is that this compilation of figures, when placed in a broader context, will provide some background for the reader to understand the physical conditions that determine when various theories are useful.

Cold atoms•Mar 18, 2013•2 citations

Books

CERN

Quantum field theory and the many body problem,

•Jan 1, 1964•0 citations

Quantum theory of many-body systems

Nicolaas Marinus Hugenholtz

In this article a survey is given of the present status of the quantum theory of many-particle systems with special emphasis on the underlying principles. Very little is said about applications. A brief introduction to some models, which are of interest for an approximate or qualitative description of actual physical systems, is followed by a discussion of two important phenomena in many-particle systems: quasi-particles and collective excitations. Next, an outline is given of mathematical methods which have been used for a precise treatment of such phenomena. A rather thorough discussion of the Bogoliubov model for interacting bosons, and the BCS model for fermions, serves as an illustration. Some new features, typical of many-particle systems, are discussed on the basis of these models. Also another approach to the many-body problem is discussed which is more logical and mathematically more rigorous. This approach differs from standard procedures in that the limit Ω-> infinity, N -> infinity is not taken at the end of the calculations but in the beginning. This quantum theory of infinite systems leads, among other things, to a better understanding of the models mentioned above.

Reports on Progress in Physics•Jul 1, 1965•112 citations

Some recent developments in the many-body problem

D. ter Haar

Summary A brief account is given of the reasons why the many-body problem has recently become the subject of a rapidly expanding literature. After a survey of the main ideas of recent theories, it is shown how these ideas have played a rôle in giving us a better understanding of such topics as superconductivity, plasmas, and liquid helium. In the theory of the many-body problem the main branches of theoretical physics applied are Hamiltonian mechanics or quantum mechanics (to describe the motion of the constituent particles of the many-body system under consideration) and statistical mechanics (to describe the collective action of the large number of particles in the system). As these subjects are relatively advanced we have discussed in an appendix the main concepts of Hamiltonian mechanics and some of those of quantum statistics, including the definition and some of the properties of fermions and bosons.

Contemporary Physics•Dec 1, 1959•3 citations

Formulation of the quantum mechanical many-body problem in terms of one- and two-particle functions

L. Szasz

Physics Letters•May 1, 1963•3 citations
One of the aims of the organisers of the FINESS conferences, and of the editors of this book, has been to encourage dialogue between researchers working in the general area of non-equilibrium superfluids. The researchers come from widely different backgrounds, and come with a broad array of favourite theoretical techniques. In this chapter we present an incomplete survey of figures from previously published papers that make a comparison between selected subsets of different theoretical methods. The goal is that this compilation of figures, when placed in a broader context, will provide some background for the reader to understand the physical conditions that determine when various theories are useful.
In this article a survey is given of the present status of the quantum theory of many-particle systems with special emphasis on the underlying principles. Very little is said about applications. A brief introduction to some models, which are of interest for an approximate or qualitative description of actual physical systems, is followed by a discussion of two important phenomena in many-particle systems: quasi-particles and collective excitations. Next, an outline is given of mathematical methods which have been used for a precise treatment of such phenomena. A rather thorough discussion of the Bogoliubov model for interacting bosons, and the BCS model for fermions, serves as an illustration. Some new features, typical of many-particle systems, are discussed on the basis of these models. Also another approach to the many-body problem is discussed which is more logical and mathematically more rigorous. This approach differs from standard procedures in that the limit Ω-> infinity, N -> infinity is not taken at the end of the calculations but in the beginning. This quantum theory of infinite systems leads, among other things, to a better understanding of the models mentioned above.
Summary A brief account is given of the reasons why the many-body problem has recently become the subject of a rapidly expanding literature. After a survey of the main ideas of recent theories, it is shown how these ideas have played a rôle in giving us a better understanding of such topics as superconductivity, plasmas, and liquid helium. In the theory of the many-body problem the main branches of theoretical physics applied are Hamiltonian mechanics or quantum mechanics (to describe the motion of the constituent particles of the many-body system under consideration) and statistical mechanics (to describe the collective action of the large number of particles in the system). As these subjects are relatively advanced we have discussed in an appendix the main concepts of Hamiltonian mechanics and some of those of quantum statistics, including the definition and some of the properties of fermions and bosons.