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Prog. Theor. Phys. Vol. 66 No. 6 (1981) pp. 2130-2146

[ Full Text PDF : FREE ACCESS (589K) ]

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

Atsushi Kuriyama and Masatoshi Yamamura*

Department of Physics, Kyushu University, Fukuoka 812
*Department of Physics, Khyoto University, Kyoto 606

(Received June 29, 1981)

Abstract:

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.


URL : http://ptp.ipap.jp/link?PTP/66/2130/
DOI : 10.1143/PTP.66.2130

[ Full Text PDF : FREE ACCESS (589K) ] Citation:

References:

  1. M. Yamamura, Prog. Theor. Phys. 33 (1965), 199[PTP].
  2. E. R. Marshalek, Nucl. Phys. A 224 (1974), 221[CrossRef].
  3. M. Yamamura amd A. Kuriyama, Prog. Theor. Phys. 65 (1981), 550[PTP].
  4. P. A. Dirac, Can. J. Math. 2 (1950), 129.
  5. A. Kuriyama and M. Yamamura, Prog. Theor. Phys. 65 (1981), 1094[PTP].
  6. R. Casalbuoni, Nuovo. Cim. A 33 (1976), 115; ibid. 33 (1976), 389.
  7. M. Yamamura, Prog. Theor. Phys. 63 (1980), 486[PTP].

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 66 No. 6 (1981) pp. 2147-2160 :
    Boson Expansion for Many-Fermion System as a Canonical Theory with Constraints. II
    Masatoshi Yamamura and Atsushi Kuriyama
  2. Progress of Theoretical Physics Vol. 67 No. 3 (1982) pp. 852-865 :
    A Classical Theory of Pairing Rotation and Intrinsic Degrees of Freedom
    Masatoshi Yamamura and Atsushi Kuriyama
  3. Progress of Theoretical Physics Vol. 67 No. 4 (1982) pp. 1122-1134 :
    A Quantal Theory of Pairing Rotation, Pairing Vibrations and Independent-Particle Motions
    Atsushi Kuriyama and Masatoshi Yamamura
  4. Progress of Theoretical Physics Vol. 67 No. 4 (1982) pp. 1135-1148 :
    A Possible Canonical Theory for Description of Pairing Correlation
    Masatoshi Yamamura and Atsushi Kuriyama
  5. Progress of Theoretical Physics Vol. 69 No. 2 (1983) pp. 681-684 :
    A Canonical Coordinate System Suitable for Adiabatic Treatment of Collective Motion
    Atsushi Kuriyama and Masatoshi Yamamura
  6. Progress of Theoretical Physics Vol. 70 No. 2 (1983) pp. 424-438 :
    Geometry of the Self-Consistent Collective-Coordinate Method for the Large-Amplitude Collective Motion
    Fumihiko Sakata, Toshio Marumori, Yukio Hashimoto and Tsutomu Une
  7. Progress of Theoretical Physics Vol. 70 No. 6 (1983) pp. 1675-1678 :
    Canonicity Condition and Its Favourite Form of Collective Hamiltonian
    Atsushi Kuriyama and Masatoshi Yamamura
  8. Progress of Theoretical Physics Vol. 71 No. 1 (1984) pp. 122-130 :
    Canonical Formulation of Time-Dpendent Hartree-Fock Method
    Atsushi Kuriyama and Masatoshi Yamamura
  9. Progress of Theoretical Physics Vol. 71 No. 4 (1984) pp. 752-774 :
    Generalization of Equation of Collective Submanifold
    Masatoshi Yamamura and Atsushi Kuriyama
  10. Progress of Theoretical Physics Vol. 72 No. 3 (1984) pp. 513-533 :
    Generalized Center of Mass and Relative Motions in Classical Many-Body System
    Masatoshi Yamamura, Atsushi Kuriyama and Shinji Iida
  11. Progress of Theoretical Physics Vol. 74 No. 1 (1985) pp. 51-65 :
    Intrinsic Excitation Modes Compatible with Large-Amplitude Collective Motion in the TDHF Theory
    Fumihiko Sakata, Toshio Marumori, Kazuhiro Muramatsu and Yukio Hashimoto
  12. Progress of Theoretical Physics Vol. 74 No. 4 (1985) pp. 693-707 :
    A Note on Collective Variables Determined by Equations of Collective Submanifold
    Masatoshi Yamamura and Atsushi Kuriyama
  13. Progress of Theoretical Physics Vol. 75 No. 2 (1986) pp. 272-287 :
    Equations of Collective Submanifold for Large Amplitude Collective Motion and Its Coupling with Intrinsic Degrees of Freedom. I
    Masatoshi Yamamura and Atsushi Kuriyama
  14. Progress of Theoretical Physics Vol. 76 No. 2 (1986) pp. 387-399 :
    Concept of Dynamical Collective Submanifold for Large-Amplitude Collective Motion in the TDHF Theory
    Fumihiko Sakata, Toshio Marumori, Yukio Hashimoto, Kazuhiro Muramatsu and Masanori Ogura
  15. Progress of Theoretical Physics Vol. 76 No. 5 (1986) pp. 1047-1059 :
    An Extension of Time-Dependent Hatree-Fock Theory Including Grassmann Variables. I
    Masatoshi Yamamura and Atsushi Kuriyama
  16. Progress of Theoretical Physics Vol. 77 No. 1 (1987) pp. 94-105 :
    Equations of Collective Submanifold for Large Amplitude Collective Motion and Its Coupling with Intrinsic Degrees of Freedom. III
    Masatoshi Yamamura and Atsushi Kuriyama
  17. Progress of Theoretical Physics Vol. 77 No. 5 (1987) pp. 1192-1208 :
    Non-Unitary Realization of the Selfconsistent Collective-Coordinate Method
    Yoshifumi R. Shimizu and Kenjiro Takada
  18. Progress of Theoretical Physics Vol. 78 No. 6 (1987) pp. 1351-1363 :
    Extraction of a Collective Submanifold for the Hénon-Heiles System
    Kunio Takabayashi
  19. Progress of Theoretical Physics Vol. 78 No. 6 (1987) pp. 1364-1391 :
    Optimum Collective Submanifold in Resonant Cases by the Self-Consistent Collective-Coordinate Method for Large-Amplitude Collective Motion
    Yukio Hashimoto, Toshio Marumori and Fumihiko Sakata
  20. Progress of Theoretical Physics Vol. 82 No. 6 (1989) pp. 1084-1105 :
    Dissipation Mechanism of the Large-Amplitude Collective Motion
    Masayuki Matsuo, Fumihiko Sakata and Toshio Marumori
  21. Progress of Theoretical Physics Vol. 85 No. 6 (1991) pp. 1235-1270 :
    Microscopic Description of Nuclear Collective Rotation by Means of the Self-Consistent Collective Coordinate Method
    Jun Terasaki, Toshio Marumori and Fumihiko Sakata
  22. Progress of Theoretical Physics Supplement No.74 & 75 (1983) pp. 66-88 :
    A Microscopic Theory of Collective and Independent-Particle Motions
    Atsushi Kuriyama
  23. Progress of Theoretical Physics Supplement No.74 & 75 (1983) pp. 89-114 :
    Boson-Fermion Expansions
    E. R. Marshalek
  24. Progress of Theoretical Physics Supplement No.74 & 75 (1983) pp. 271-281 :
    An Extension of TDHF and Boson-Fermion Expansion
    Masatoshi Yamamura
  25. Progress of Theoretical Physics Supplement No.93 (1987) pp. 1-175 :
    Time-Dependent Hartree-Fock Method and Its Extension
    Masatoshi Yamamura and Atsushi Kuriyama
  26. Progress of Theoretical Physics Supplement No.141 (2001) pp. 179-241 :
    Non-Unitary Boson Mapping and Its Application to Nuclear Collective Motions
    Kenjiro Takada

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