Collective Description of a System of Interacting Bose Particles. I

Sunakawa, Sigenobu; Yokoo, Yoshimatsu; Nakatani, Hiroshi

doi:10.1143/ptp.27.589

Cited by 31 publications

(19 citation statements)

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“…This is just the same form as that obtained by Sunakawa [9] except that there exists the last constant term proportional to p p…”

Section: Exact Canonically Conjugate Momentasupporting

confidence: 61%

“…The result (5.5) is not identical with the Sunakawa's result [9] for a Bose system. This is because we have dealt with a Fermi system.…”

contrasting

confidence: 61%

“…These commutation relations have quite the same structures as those of the commutation relations obtained at the first stage in the Sunakawa's discrete integral equation method [9]. As is shown from (2.18), the right-hand side (RHS) of the second line does not take the value − i δ kk ′ and the third one does not vanish.…”

Section: Introductionsupporting

confidence: 52%

“…This type of the discrete integral equation was first presented in the Sunakawa's second quantized collective formalism for an interacting Bose system [9]. It was also proposed by us and one of the present author's (S.N.)…”

Section: Exact Canonically Conjugate Momentamentioning

confidence: 59%

“…Their ideas have the advantage of being exactly solvable [23,24]. While the Sunakawa's approach for a Fermi system [9] also may be anticipated to work well for such a problem. In this paper, on the isospin space (T, T z ), we define a density operator ρ T,Tz k and further following Tomonaga, introduce a collective momentum.…”

Section: Introductionmentioning

confidence: 99%

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

Nishiyama

Providência

2015

Int. J. Mod. Phys. E

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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.

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“…This is just the same form as that obtained by Sunakawa [9] except that there exists the last constant term proportional to p p…”

Section: Exact Canonically Conjugate Momentasupporting

confidence: 61%

“…The result (5.5) is not identical with the Sunakawa's result [9] for a Bose system. This is because we have dealt with a Fermi system.…”

contrasting

confidence: 61%

Section: Introductionsupporting

confidence: 52%

Section: Exact Canonically Conjugate Momentamentioning

confidence: 59%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Nishiyama

Providência

2015

Int. J. Mod. Phys. E

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A density functional representation of quantum chemistry. II. Local quantum field theories of molecular matter in terms of the charge density operator do not work

Primas

Schleicher

1975

Int J of Quantum Chemistry

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AbstractsA comprehensive review of the attempts to rephrase molecular quantum mechanics in terms of the particle density operator and the current density or phase density operator is given. All pertinent investigations which have come to our attention suffer from severe mathematical inconsistencies and are not adequate to the few-body problem of quantum chemistry. The origin of the failure of these attempts is investigated and it is shown that a realization of a local quantum field theory of molecular matter in terms of observables would presuppose the solution of many highly nontrivial mathematical problems.Dans une revue dttaillte de la IittCrature nous exposons les tentatives de reformuler la mtcanique quantique molCculaire directement ? i I'aide des optrateurs de densitt de particules, de courant ou de phase. Tous les travaux consider& comportent dimportantes inconsistences mathkmatiques et ne sont pas adaptables au problkme pluricorps de la chimie quantique. A la suite d'une Ctude sur les raisons de cet Cchec on montre que la rtalisation d'une thCorie de champs quantique local en termes d'observables implique la rtsolution de nombreux problkmes mathkmatiques qui w i t loin5 d'ctre triviauu.

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Excitations in Superfluid Helium

Ruvalds

1974

Elementary Excitations in Solids, Molecules, and Atom

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Collective Description of a System of Interacting Bose Particles. I

Cited by 31 publications

References 0 publications

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

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

A density functional representation of quantum chemistry. II. Local quantum field theories of molecular matter in terms of the charge density operator do not work

Excitations in Superfluid Helium

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