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

Progress of Theoretical Physics

An Extension of Time-Dependent Hatree-Fock Theory Including Grassmann Variables. I: --Basic Formulation in the Framework of Dirac's Canonical Theory with Constraints--

M. Yamamura, A. Kuriyama

Published Nov 1, 1986• 1 citation
Publisher

Abstract

A microscopic theory of collective and independent-particle motions in many-fermion system is developed in the framework of Dirac's canonical theory with constraints.The basic idea is an extension of the conventional time-dependent Hartree-Fock theory based on the use of the Grassmann variables and, in certain sense, it supplements incomplete parts of the paper presented by the present authors.Canonicity condition to certify the canonical property of the variables, equation to determine collective submanifold and constraints to govern the collective and the Grassmann variables are given.

DOI
10.1143/ptp.76.1047

Related papers

A Microscopic Theory of Collective and Independent-Particle Motions

M. Yamamura, A. Kuriyama

A microscopic theory of collective and independent-particle motion in many-fermion system is developed in the framework of the classical theory. The basic idea is an extension of the conventional time-dependent Hartree-Fock method with the use of fermion coherent state representation. Equation to determine collective path and constraints to govern the collective and the independent-particle variables are given. Hamiltonian and other physical quantities given with the original fermion variables are rewritten to the forms expressed in terms of the collective and the independent-particle variables.

Progress of Theoretical Physics•Feb 1, 1981•17 citations

Equations of Collective Submanifold for Large Amplitude Collective Motion and Its Coupling with Intrinsic Degrees of Freedom. III

M. Yamamura, A. Kuriyama

From the viewpoint defferent from that of Part I, the time-dependent Harteree-Fock theory is formulated for describing large amplitude collective motion and its coupling with intrinsic degrees of freedom. The basic idea consists of the introduction of an additional degree of freedom for the collective motion and the use of Dirac’s canonical theory with constraints. The formalism is essentially equivalent to the ordinary time-dependent Hartree-Fock theory presented in Part I. The result given in Part I is completely reproduced.

Progress of Theoretical Physics•Jan 1, 1987•5 citations

Boson Expansion for Many-Fermion System as a Canonical Theory with Constraints. I

A. Kuriyama, M. Yamamura

A classical theory for many-fermion system is presented in the canonical form by introducing the ordinary and the Grassmann variables, the number of which exceeds “apparently” the original one. The basic idea is a translation of a theory proposed by the present authors for the case of the particle-hole pairs to the case of the Hartree-Bogoliubov type pairs. Certain constraints governing the variables are introduced and the double counting in the number of the degrees of freedom concerning the extra variables can be avoided. The quantization is performed with the aid of the Dirac bracket to take account of the constraints. It is shown that final result is completely identical with the compact form of the boson expansion given by Marshalek.

Progress of Theoretical Physics•Dec 1, 1981•17 citations

An Extension of Time-Dependent Hartree-Fock Theory Including Grassmann Variables. II: --Canonical Invariance and Specification of Coordinate System--

M. Yamamura, A. Kuriyama

Properties of the basic eqations derived in Part (I) are investigated. Especially, it is stressed that the equations are invariant for symplectic and special orthogonal transformation. Further, it is discussed how to specify coordinate system. Initial condition for solving the basic equation is also shown.

Progress of Theoretical Physics•Nov 1, 1986•0 citations

Canonical Formulation of Time-Dependent Hartree-Fock Method

A. Kuriyama, M. Yamamura

On the basis of a canonical formulation of full time-dependent Hartree-Fock method, we develop a formulation of time-dependent Hartree-Fock method for the description of collective motion in a completely canonical form.In the derivation of basic equations, the general form of canonicity condition plays an important role.

Progress of Theoretical Physics•Jan 1, 1984•4 citations

Boson Expansion for Many-Fermion System as a Canonical Theory with Constraints. II

M. Yamamura, A. Kuriyama

With the use of the ordinary and the Grassmann variables, a classical theory for many-fermion system with particle-hole correlations is presented in a canonical form. This system involves many valence particles/holes in addition to many particle-hole pairs. The particle-hole pairs are assigned as the collective degree of freedom and the others as the independent-particle one. In order to avoid the double counting in the number of the degrees of freedom due to the introduction of the collective variables, certain constraints are introduced. The quantization is performed with the aid of the Dirac theory for canonical system with constraints. It is shown that the result is completely equivalent to that obtained with the use of the boson expansion method by Marshalek.

Progress of Theoretical Physics•Dec 1, 1981•6 citations
A microscopic theory of collective and independent-particle motions in many-fermion system is developed in the framework of Dirac's canonical theory with constraints.The basic idea is an extension of the conventional time-dependent Hartree-Fock theory based on the use of the Grassmann variables and, in certain sense, it supplements incomplete parts of the paper presented by the present authors.Canonicity condition to certify the canonical property of the variables, equation to determine collective submanifold and constraints to govern the collective and the Grassmann variables are given.
A microscopic theory of collective and independent-particle motion in many-fermion system is developed in the framework of the classical theory. The basic idea is an extension of the conventional time-dependent Hartree-Fock method with the use of fermion coherent state representation. Equation to determine collective path and constraints to govern the collective and the independent-particle variables are given. Hamiltonian and other physical quantities given with the original fermion variables are rewritten to the forms expressed in terms of the collective and the independent-particle variables.
From the viewpoint defferent from that of Part I, the time-dependent Harteree-Fock theory is formulated for describing large amplitude collective motion and its coupling with intrinsic degrees of freedom. The basic idea consists of the introduction of an additional degree of freedom for the collective motion and the use of Dirac’s canonical theory with constraints. The formalism is essentially equivalent to the ordinary time-dependent Hartree-Fock theory presented in Part I. The result given in Part I is completely reproduced.
A classical theory for many-fermion system is presented in the canonical form by introducing the ordinary and the Grassmann variables, the number of which exceeds “apparently” the original one. The basic idea is a translation of a theory proposed by the present authors for the case of the particle-hole pairs to the case of the Hartree-Bogoliubov type pairs. Certain constraints governing the variables are introduced and the double counting in the number of the degrees of freedom concerning the extra variables can be avoided. The quantization is performed with the aid of the Dirac bracket to take account of the constraints. It is shown that final result is completely identical with the compact form of the boson expansion given by Marshalek.
With the use of the ordinary and the Grassmann variables, a classical theory for many-fermion system with particle-hole correlations is presented in a canonical form. This system involves many valence particles/holes in addition to many particle-hole pairs. The particle-hole pairs are assigned as the collective degree of freedom and the others as the independent-particle one. In order to avoid the double counting in the number of the degrees of freedom due to the introduction of the collective variables, certain constraints are introduced. The quantization is performed with the aid of the Dirac theory for canonical system with constraints. It is shown that the result is completely equivalent to that obtained with the use of the boson expansion method by Marshalek.