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

On the Exact Canonical Conjugate Momenta of Collective Motion in Many-Boson System

Masayoshi Nakamura, Ryō Suzuki

Published Sep 1, 1980• 3 citations
Publisher

Abstract

The exact canonical momenta conjugate to collective coordinates are proposed for the description of quantum-mechanical collective motion in a ment-boson system. The present procedure gives rise to the possibility of extension of Tomonaga's theory to the three-dimensional case.
DOI
10.1143/ptp.64.1086

Related papers

EXACT CANONICALLY CONJUGATE MOMENTA APPROACH TO AN SU (N) QUANTUM SYSTEM

Seiya Nishiyama

The collective field formalism by Jevicki and Sakita is a useful approach to the problem of treating general planar diagrams involved in an SU (N) symmetric quantum system. To approach this problem, standing on the Tomonaga spirit we also previously developed a collective description of an SU (N) symmetric Hamiltonian. However, this description has the following difficulties: (i) Collective momenta associated with the time derivatives of collective variables are not exact canonically conjugate to the collective variables; (ii) The collective momenta are not independent of each other. We propose exact canonically conjugate momenta to the collective variables with the aid of the integral equation method developed by Sunakawa et al. A set of exact canonical variables which are derived by the first quantized language is regarded as a natural extension of the Sunakawa et al.'s to the case for the SU (N) symmetric quantum system. A collective Hamiltonian is represented in terms of the exact canonical variables up to the order of [Formula: see text].

International Journal of Modern Physics A•Dec 30, 1998•2 citations

Exact canonically conjugate momenta approach to a one-dimensional neutron–proton system, I

Seiya Nishiyama, João da Providência

Introducing collective variables, a collective description of nuclear surface oscillations has been developed with the first-quantized language, contrary to the second-quantized one in Sunakawa's approach for a Bose system. It overcomes difficulties remaining in the traditional theories of nuclear collective motions: Collective momenta are not exact canonically conjugate to collective coordinates and are not independent. On the contrary to such a description, Tomonaga first gave the basic idea to approach elementary excitations in a one-dimensional Fermi system. The Sunakawa's approach for a Fermi system is also expected to work well for such a problem. In this paper, on the isospin space, we define a density operator and further following Tomonaga, introduce a collective momentum. We propose an exact canonically momenta approach to a one-dimensional neutron–proton (N–P) system under the use of the Grassmann variables.

arXiv:1410.3081•International Journal of Modern Physics E•Jun 1, 2015•2 citations

Collective Description of a System of Interacting Bose Particles. I

Sigenobu Sunakawa, Yoshimatsu Yokoo, Hiroshi Nakatani

The collective description of the one-dimensional interacting Bose system is studied. The exact canonical conjugate of the density operator is given explicitly. The Hamiltonian of the system is expressed in terms of the exact collective variables.

Progress of Theoretical Physics•Mar 1, 1962•28 citations

Collective motions in nuclei and the spectrum generating algebras T5 × SO(3), GL(3,R), and CM(3)

P. Gulshani, DAVID J. ROWE

Cusson's classical treatment of the collective rotations of a discrete system of N particles is extended to the full quantum mechanical system by means of a straightforward generalization of Villars' canonical transformation. In this manner, Bohr's collective Hamiltonian, with various values for the rotational mass, is microscopically derived. The nature and criteria for the existence of various collective flows in a many-body system are also given. The collective parts of the Hamiltonian are then separately expressed in original particle coordinates and momenta and in this manner the possibility of microscopic calculations for the collective motions is suggested. Finally appropriate microscopic Hamiltonians for the S.G.A.'s T5 × SO(3), GL(3,R), and CM(3) are determined.

Canadian Journal of Physics•May 1, 1976•67 citations

Applicability of the Canonical Quantization Procedure for the Collective Hamiltonian Derived by the Selfconsistent-Collective-Coordinate Method

Masayuki Matsuo, K. Matsuyanagi

We investigate the validity of the canonical quantization of the collective Hamiltonian derived by the selfconsistent-collective-coordinate method. Special attention is paid to the boundary condition for the (η*, η) expansion, which fixes the canonical coordinate system to carry out the quantization procedure. We remove the ambiguity of the boundary condition by requiring that the boson representations obtained by the canonical quantization agree, to the order 1/Ω, with those derived by the modified-Marumori boson-expansion method in a certain limit. Numerical examples for an exactly solvable model show that our quantization procedure provides us with remarkably accurate results.

Progress of Theoretical Physics•Aug 1, 1985•18 citations

On exact canonical momenta of collective motion in a many-boson system

Masayoshi Nakamura

Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B•Jan 1, 1983•1 citation
The collective field formalism by Jevicki and Sakita is a useful approach to the problem of treating general planar diagrams involved in an SU (N) symmetric quantum system. To approach this problem, standing on the Tomonaga spirit we also previously developed a collective description of an SU (N) symmetric Hamiltonian. However, this description has the following difficulties: (i) Collective momenta associated with the time derivatives of collective variables are not exact canonically conjugate to the collective variables; (ii) The collective momenta are not independent of each other. We propose exact canonically conjugate momenta to the collective variables with the aid of the integral equation method developed by Sunakawa et al. A set of exact canonical variables which are derived by the first quantized language is regarded as a natural extension of the Sunakawa et al.'s to the case for the SU (N) symmetric quantum system. A collective Hamiltonian is represented in terms of the exact canonical variables up to the order of [Formula: see text].
Introducing collective variables, a collective description of nuclear surface oscillations has been developed with the first-quantized language, contrary to the second-quantized one in Sunakawa's approach for a Bose system. It overcomes difficulties remaining in the traditional theories of nuclear collective motions: Collective momenta are not exact canonically conjugate to collective coordinates and are not independent. On the contrary to such a description, Tomonaga first gave the basic idea to approach elementary excitations in a one-dimensional Fermi system. The Sunakawa's approach for a Fermi system is also expected to work well for such a problem. In this paper, on the isospin space, we define a density operator and further following Tomonaga, introduce a collective momentum. We propose an exact canonically momenta approach to a one-dimensional neutron–proton (N–P) system under the use of the Grassmann variables.
Cusson's classical treatment of the collective rotations of a discrete system of N particles is extended to the full quantum mechanical system by means of a straightforward generalization of Villars' canonical transformation. In this manner, Bohr's collective Hamiltonian, with various values for the rotational mass, is microscopically derived. The nature and criteria for the existence of various collective flows in a many-body system are also given. The collective parts of the Hamiltonian are then separately expressed in original particle coordinates and momenta and in this manner the possibility of microscopic calculations for the collective motions is suggested. Finally appropriate microscopic Hamiltonians for the S.G.A.'s T5 × SO(3), GL(3,R), and CM(3) are determined.
We investigate the validity of the canonical quantization of the collective Hamiltonian derived by the selfconsistent-collective-coordinate method. Special attention is paid to the boundary condition for the (η*, η) expansion, which fixes the canonical coordinate system to carry out the quantization procedure. We remove the ambiguity of the boundary condition by requiring that the boson representations obtained by the canonical quantization agree, to the order 1/Ω, with those derived by the modified-Marumori boson-expansion method in a certain limit. Numerical examples for an exactly solvable model show that our quantization procedure provides us with remarkably accurate results.