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Prog. Theor. Phys. Vol. 57 No. 5 (1977) pp. 1554-1571

[ Full Text PDF : FREE ACCESS (1481K) ]

A New Fermion Many-Body Theory Based on the SO(2N+1) Lie Algebra of the Fermion Operators

Hideo Fukutome, Masatoshi Yamamura and Seiya Nishiyama*

Department of Physics, Kyoto University, Kyoto 606
*Department of Physics, Kochi University, Kochi 780

(Received October 14, 1976)

Abstract:

A new many-body theory for fermions is proposed wihich is based on the SO(2N+1) Lie algebra of the fermion operators consisted of the annihilation-creation operators and the pair operators. A New cannonical transformation, which is the extension of the Bogoliubov transformation to the SO(2N+1) group, is introduced. A new bose representation for the fermion Lie operators is obtained by mapping the fermion Lie operators into the regular representation of the SO(2N+1) group. The annihilation-creation operators and the pair operators of fermions are represented by the closed first order differential operators on the SO(2N+1) group. An exact representation of fermion wavefunctions in a form similar to the wavefunction of the generator coordinate method is obtained making use of the SO(2N+1) canonical transformation. The physical fermion space is shown to be the irreducible spinor representation of the SO(2N+1) group. The dynamics of fermions in the bose representation space is shown to represent rotations of a 2N+1 dimensional rotator.


URL : http://ptp.ipap.jp/link?PTP/57/1554/
DOI : 10.1143/PTP.57.1554

[ Full Text PDF : FREE ACCESS (1481K) ] Citation:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 58 No. 6 (1977) pp. 1692-1708 :
    On the SO(2N+1) Regular Representation of Operators and Wave Functions of Fermion Many-Body Systems
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  2. Progress of Theoretical Physics Vol. 60 No. 6 (1978) pp. 1624-1639 :
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  3. Progress of Theoretical Physics Vol. 63 No. 2 (1980) pp. 486-497 :
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  4. Progress of Theoretical Physics Vol. 64 No. 2 (1980) pp. 558-567 :
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  5. Progress of Theoretical Physics Vol. 64 No. 6 (1980) pp. 2076-2090 :
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  6. Progress of Theoretical Physics Vol. 65 No. 2 (1981) pp. 550-564 :
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  7. Progress of Theoretical Physics Vol. 65 No. 3 (1981) pp. 809-827 :
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  8. Progress of Theoretical Physics Vol. 66 No. 1 (1981) pp. 348-350 :
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  9. Progress of Theoretical Physics Vol. 68 No. 2 (1982) pp. 680-683 :
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  10. Progress of Theoretical Physics Vol. 69 No. 1 (1983) pp. 100-112 :
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  11. Progress of Theoretical Physics Vol. 69 No. 6 (1983) pp. 1811-1814 :
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  12. Progress of Theoretical Physics Vol. 71 No. 1 (1984) pp. 122-130 :
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  13. Progress of Theoretical Physics Vol. 71 No. 4 (1984) pp. 752-774 :
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  14. Progress of Theoretical Physics Vol. 71 No. 5 (1984) pp. 973-984 :
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  15. Progress of Theoretical Physics Vol. 72 No. 2 (1984) pp. 239-251 :
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  16. 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
  17. Progress of Theoretical Physics Vol. 85 No. 6 (1991) pp. 1211-1222 :
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    Seiya Nishiyama and Hideo Fukutome
  18. Progress of Theoretical Physics Vol. 96 No. 5 (1996) pp. 1043-1048 :
    Note on the Improper Bogoliubov Transformation
    Masaharu Iwasaki
  19. Progress of Theoretical Physics Supplement No.71 (1981) pp. 1-47 :
    Chapter 1. Present Status of the Microscopic Study of Low-Lying Collective States in Spherical and Transitional Nuclei
    Toshio Marumori, Kenjiro Takada and Fumihiko Sakata
  20. Progress of Theoretical Physics Supplement No.74 & 75 (1983) pp. 66-88 :
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  21. Progress of Theoretical Physics Supplement No.80 (1984) pp. 62-75 :
    Methods of Dynamical Lie Algebra for Many Fermion Green Functions
    Joseph L. Birman and Allan I. Solomon

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