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

Journal of Physics A Mathematical and General

Renormalised perturbation theory of normal systems

Colin John Lambert, W. E. Hagston

Published Jul 1, 1981• 4 citations
Publisher

Abstract

Employing an infinite hierarchy of equations for the Green functions of a many particle system in its ground state mod psi N ), the well known non-relativistic, time-dependent, ground-state perturbation theory of a normal system of interacting fermions is derived, without introducing the hypothesis that mod psi N ) is the adiabatic transform of a non-interacting state. This new formulation of the problem allows us to renormalise conventional perturbation theory by introducing an effective interaction Gamma and the final result is a highly summed and manifestly self-consistent perturbation expansion in powers of Gamma . The authors calculate Gamma to second order and demonstrate that many of the well known results of time-dependent perturbation theory may be obtained by choosing the simplest approximations for Gamma . The results are readily generalised to finite temperatures and the formalism provides a generalised form of Hartree-Fock theory which may have important applications in many areas of physics.

DOI
10.1088/0305-4470/14/7/010

Related papers

Renormalised perturbation theory of ordered systems

W. E. Hagston, Colin John Lambert

Introduces a new self-consistent summation procedure for the analysis of Feynman-Dyson perturbation series and demonstrate how a self-consistent expression for the self-energies of an interacting system may be obtained. The authors obtain the simplest self-consistent solution to the problem of an interacting many fermion system exhibiting long-range order, characterised by the existence of anomalous propagators, in which correlation effects not described by the Hartree-Fock-Gorkov approximation are important.

Journal of Physics A Mathematical and General•Aug 1, 1981•1 citation

A hierarchy of equations for finite temperature Green functions

Colin John Lambert

Abstract Employing a new theorem on time ordered products of operators, an infinite hierarchy of equations for the finite temperature Green functions of a many particle system is obtained. The analysis provides a basis for the extension to finite temperatures of recent results from ground state perturbation theory. The connection between the present analysis and the corresponding ground state formalism is briefly discussed.

physica status solidi (b)•Oct 1, 1981•0 citations

Perturbation Theory for an Infinite Medium of Fermions. III. Derivation of the Landau Theory of Fermi Liquids

Abraham Klein

The methods employed in the previous papers of this series for the ground-state energy of a normal Fermion system are extended to finite temperatures. The basic assumption is that the density matrix of the actual system in thermodynamic equilibrium can be derived by adiabatic transformation from the density matrix of system of noninteracting particles at the same temperature, volume, and chemical potential. However, the spectrum of the noninteracting system must be dependent on the intensive parameters. The self-consistency of the scheme is exhibited by demonstrating that the effective potential characterizing this system can be related to the self-energy operator of the actual system. Two equivalent versions of the theory are derived. In one of these the basic equations are precisely those of the Landau theory of Fermi liquids with the difference, however, that all quantities are given explicitly from first principles.

Physical Review•Feb 15, 1961•16 citations

Many-body Theory Exposed! Propagator Description of Quantum Mechanics in Many-body Systems

Willem H Dickhoff, Dimitri Van Neck

Identical Particles Second Quantization Independent-Particle Model for Fermions in Finite Systems Two-Particle States and Interactions Noninteracting Bosons and Fermions Propagators in One-Particle Quantum Mechanics Single-Particle Propagator in Many-Particle Systems Perturbation Expansion of the Single-Particle Propagator Dyson Equation and Self-consistent Green's Functions Mean-Field or Hartree-Fock Approximation Beyond the Mean-Field Approximation Interacting Boson Systems Excited States in Finite Systems Excited States in Infinite Systems Excited States in N 2 Systems and In-Medium Scattering Dynamical Treatment of the Self-energy in Infinite Systems Dynamical Treatment of the Self-energy in Finite Systems Bogoliubov Perturbation Expansion for the Bose Gas Boson Perturbation Theory Applied to Physical Systems In-Medium Interaction and Scattering of Dressed Particles Conserving Approximations and Excited States Pairing Phenomena Propagator Framework for Phenomenological Description of Many-Body Systems Finite Temperature Formalism and Applications.

•Aug 20, 2005•49 citations

Optimised mean fields for atoms. I. Mean-field methods for the description of N-fermion systems

Klaus Dietz, Olaf Lechtenfeld, G Weymans

Siegert's representation (1960) for the grand canonical partition function of a fermion system with two-particle interactions serves as a starting point for a perturbation expansion around stationary points. It is shown that, in general, the latter are given by solutions of the time-independent Hartree equation. Introducing more general random fields, exchange terms are obtained in the stationarity equation. The procedure is extended to relativistic systems. A perturbative expansion for e.g. the ground-state energy of the N-particle relativistic bound-state problem is obtained which allows, contrary to 'Hamiltonian methods', a straightforward application of standard regularisation and renormalisation procedures.

Journal of Physics B Atomic and Molecular Physics•Dec 14, 1982•35 citations

Perturbation theory for double-time temperature-dependent Green functions

Sergei Vladimirovich Tyablikov, В. Л. Бонч-Бруевич

(by translator) A perturbation theory is developed for normal many-particle systems by expanding the inverse of the advanced and retarded Green functions. Both systems with direct interactions and systems with interactions through a quantum field are considered. For the former, the infinite set of coupled equations is written down and the various methods of decoupling discussed. Systems with weak, hard sphere type, or coulomb interactions are considered and the connections with other methods discussed. For systems with quantum field interactions, the chain of equations involves both fermion and boson Green functions and the first approximation can be much better than in earlier cases. This latter approach seems to be more convenient when collective oscillations are important.

Advances In Physics•Oct 1, 1962•56 citations
Employing an infinite hierarchy of equations for the Green functions of a many particle system in its ground state mod psi N ), the well known non-relativistic, time-dependent, ground-state perturbation theory of a normal system of interacting fermions is derived, without introducing the hypothesis that mod psi N ) is the adiabatic transform of a non-interacting state. This new formulation of the problem allows us to renormalise conventional perturbation theory by introducing an effective interaction Gamma and the final result is a highly summed and manifestly self-consistent perturbation expansion in powers of Gamma . The authors calculate Gamma to second order and demonstrate that many of the well known results of time-dependent perturbation theory may be obtained by choosing the simplest approximations for Gamma . The results are readily generalised to finite temperatures and the formalism provides a generalised form of Hartree-Fock theory which may have important applications in many areas of physics.
Introduces a new self-consistent summation procedure for the analysis of Feynman-Dyson perturbation series and demonstrate how a self-consistent expression for the self-energies of an interacting system may be obtained. The authors obtain the simplest self-consistent solution to the problem of an interacting many fermion system exhibiting long-range order, characterised by the existence of anomalous propagators, in which correlation effects not described by the Hartree-Fock-Gorkov approximation are important.
The methods employed in the previous papers of this series for the ground-state energy of a normal Fermion system are extended to finite temperatures. The basic assumption is that the density matrix of the actual system in thermodynamic equilibrium can be derived by adiabatic transformation from the density matrix of system of noninteracting particles at the same temperature, volume, and chemical potential. However, the spectrum of the noninteracting system must be dependent on the intensive parameters. The self-consistency of the scheme is exhibited by demonstrating that the effective potential characterizing this system can be related to the self-energy operator of the actual system. Two equivalent versions of the theory are derived. In one of these the basic equations are precisely those of the Landau theory of Fermi liquids with the difference, however, that all quantities are given explicitly from first principles.
Identical Particles Second Quantization Independent-Particle Model for Fermions in Finite Systems Two-Particle States and Interactions Noninteracting Bosons and Fermions Propagators in One-Particle Quantum Mechanics Single-Particle Propagator in Many-Particle Systems Perturbation Expansion of the Single-Particle Propagator Dyson Equation and Self-consistent Green's Functions Mean-Field or Hartree-Fock Approximation Beyond the Mean-Field Approximation Interacting Boson Systems Excited States in Finite Systems Excited States in Infinite Systems Excited States in N 2 Systems and In-Medium Scattering Dynamical Treatment of the Self-energy in Infinite Systems Dynamical Treatment of the Self-energy in Finite Systems Bogoliubov Perturbation Expansion for the Bose Gas Boson Perturbation Theory Applied to Physical Systems In-Medium Interaction and Scattering of Dressed Particles Conserving Approximations and Excited States Pairing Phenomena Propagator Framework for Phenomenological Description of Many-Body Systems Finite Temperature Formalism and Applications.
Siegert's representation (1960) for the grand canonical partition function of a fermion system with two-particle interactions serves as a starting point for a perturbation expansion around stationary points. It is shown that, in general, the latter are given by solutions of the time-independent Hartree equation. Introducing more general random fields, exchange terms are obtained in the stationarity equation. The procedure is extended to relativistic systems. A perturbative expansion for e.g. the ground-state energy of the N-particle relativistic bound-state problem is obtained which allows, contrary to 'Hamiltonian methods', a straightforward application of standard regularisation and renormalisation procedures.
(by translator) A perturbation theory is developed for normal many-particle systems by expanding the inverse of the advanced and retarded Green functions. Both systems with direct interactions and systems with interactions through a quantum field are considered. For the former, the infinite set of coupled equations is written down and the various methods of decoupling discussed. Systems with weak, hard sphere type, or coulomb interactions are considered and the connections with other methods discussed. For systems with quantum field interactions, the chain of equations involves both fermion and boson Green functions and the first approximation can be much better than in earlier cases. This latter approach seems to be more convenient when collective oscillations are important.