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

Physical Review C

Path integral approach for many-fermion systems and an extension of the time-dependent Hartree-Fock method

Kazunari Kaneko

Published Aug 1, 1984• 6 citations
Publisher

Abstract

The quantization of an extended time-dependent Hartree-Fock equation is performed by using the path integral formalism. The path integral form of time evolution operator between initial and final states is obtained with the use of the completeness relation of the fermion coherent states. It is shown that the extended time-dependent Hartree-Fock equation is naturally derived as a classical limit of the path integral.

DOI
10.1103/physrevc.30.723

Related papers

A Path Integral Formalism of Collective Motion

Hiroshi Kuratsuji

A Quantum mechanical formalism of collective motion is proposed by using the idea of path integral method. Time evolution of many· body system is described by the propagator which joins the many-body state vectors parametrized by complex collective parameters. A general form of path integral representation for the propagator is derived in the complex parameter space. In particular the case of the coherent state representation is discussed in detail. It is pointed out that the time-dependent variation principle and especially the time dependent Hartree-Fock are naturally obtained as a classical limit.

Progress of Theoretical Physics•Jan 1, 1981•16 citations

Path Integral Approach to Semiclassical Bound State for Many-Fermion Systems: Harmonic Approximation around Static H-F Solutions

Hiroshi Kuratsuji

We give a preliminary report on the bound state quantization of many-fermion systems based on the semiclassical expansion of the path integral in the generalized coherent state representation. As a particular case we consider the quantization around static Hartree-Fock solutions, which reproduces the RPA spectrum such that the correlation energy is naturally included.

Progress of Theoretical Physics•Sep 1, 1983•0 citations

Path integrals and time-dependent mean-field theories

Jean-Paul Blaizot, Henri Orland

We present a path integral formulation of the many-body problem, using a continuous and overcomplete set of vectors in the Hilbert space. The saddle-point approximation for the calculation of the functional integral leads to classical equation of motion which can be quantized in a well prescribed way. The time dependent Hartree-Fock equations are an example of such classical equations. They are obtained by integrating over an overcomplete set of Slater determinant.

Journal de Physique Lettres•Jan 1, 1980•20 citations

Exact Stochastic Mean-Field Approach to the Fermionic Many-Body Problem

Olivier Juillet, Ph. Chomaz

We investigate a reformulation of the dynamics of interacting fermion systems in terms of a stochastic extension of time-dependent Hartree-Fock equations. From a path-integral representation of the evolution operator, we show that the exact N-body state can be interpreted as a coherent average over Slater determinants evolving in a random mean-field. The imaginary time propagation is also presented and gives a similar scheme which converges to the exact ground state. In addition, the growth of statistical errors is examined to show the stability of this stochastic formulation.

arXiv:nucl-th/0104085•Physical Review Letters•Mar 22, 2002•45 citations

Path Integral on the Coset Space of the SO(2N) Group and the Time-Dependent Hartree-Bogoliubov Equation

S. Nishiyama

A quantized time-dependent Hartree-Bogoliubov (TDHB) theory of many fermion systems with pair correlations is presented. It is obtained not by using a priori quantized method but by using the path integrals on the coset space SO(2N)/U(N). Then we can get another version of the TDHB equation expressed through the coset variables in a natural way as a classical limit.

Progress of Theoretical Physics•Jul 1, 1981•14 citations

The Hartree-Fock State and Fermion Path-Integral

Jun Ishida

Following the path-integral formalism by Ohnuki and Kashiwa, we calculate the transition amplitude exactly for a model which has four-fermi type interaction. We also investigate the time development of the expectation value of field operator to see to what extent the classical correspondence works in quantum mechanics of fermions.

Progress of Theoretical Physics•Feb 1, 1981•2 citations
The quantization of an extended time-dependent Hartree-Fock equation is performed by using the path integral formalism. The path integral form of time evolution operator between initial and final states is obtained with the use of the completeness relation of the fermion coherent states. It is shown that the extended time-dependent Hartree-Fock equation is naturally derived as a classical limit of the path integral.
A Quantum mechanical formalism of collective motion is proposed by using the idea of path integral method. Time evolution of many· body system is described by the propagator which joins the many-body state vectors parametrized by complex collective parameters. A general form of path integral representation for the propagator is derived in the complex parameter space. In particular the case of the coherent state representation is discussed in detail. It is pointed out that the time-dependent variation principle and especially the time dependent Hartree-Fock are naturally obtained as a classical limit.
We investigate a reformulation of the dynamics of interacting fermion systems in terms of a stochastic extension of time-dependent Hartree-Fock equations. From a path-integral representation of the evolution operator, we show that the exact N-body state can be interpreted as a coherent average over Slater determinants evolving in a random mean-field. The imaginary time propagation is also presented and gives a similar scheme which converges to the exact ground state. In addition, the growth of statistical errors is examined to show the stability of this stochastic formulation.