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Chinese Physics C > 1982, Vol. 6 > Issue(5): 630-641

THESU2×SU2BASIS AND THE PHYSICAL BASES FOR THE STATE VECTORS OF d-BOSON SYSTEMS AND THE TRACELESS BOSON OPERATORS (Ⅰ)

  • Department of Physics, Peking University

  • The group chain U 5 O 5 SU 2× SU 2used by K. T. Hecht (1965) and by the othersprovides an important representation for expressing the physical basis of d-boson sys-tems. However the methods which have been introduced for this SU 2× SU 2representa-tion to construct a physical basis is poorer in comparison with those for the otherrepresentations. In view of this we try to find appropriate methods to obtain the SU 2× SU 2representation wave functions of the existing physical bases constructed byChacon et al. and by Szpikowski et al., In the present paper we analyse the SU 2× SU 2tensor properties of the,bosonoperators and Vilenkin's traceless boson operators and express succinctly the elementaryvectors of the SU 2× SU 2basis, the |PP SU 2× SU 2> vectors, in terms of the tracelessoperators. With the help of this form of the| PP SU 2SU 2> vectors we derive a simpleformula for obtaining the SU 2× SU 2-representation wave functions of a physical basisfrom its ( nμ)-representation wave functions. Thus the problem mentioned above is partlysolved. The other parts of the solution of the problem will be found in a coming paper.
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    [1] D.B Bès, Nucl. Phys., 10(1959), 373.[2」E. Chaon, M. Moehineky and R. T, Sharp, J. Math. Phys., 17 (1976), 668.[3]N. Y. Vilenkin, Special Functions and Theory of Groups Representations(A.M. Tranl. Providence, B. I, 1968).[4]M. A. Lohe, "The Development of the Boson Calcnlns for the Otthogonal and Symplectic Groups" Thesis, University of Adelaide (1974).[5]E. Chaón and M. Moshinsky, J. Math. Phys., 18(1977), 870.[6]S. Szpikowski and A. Gózdz, Nucl. Phys., A340(1980),76.[7]K. T. Hecht, Nucl. Phys., 63(1965), 117.[8]孙洪洲, 高能物理与核物理, 4(1980), 478.

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YANG ZE-SEN and TSE-SEN YANG. THE SU 2× SU 2BASIS AND THE PHYSICAL BASES FOR THE STATE VECTORS OF d-BOSON SYSTEMS AND THE TRACELESS BOSON OPERATORS (Ⅰ)[J]. Chinese Physics C, 1982, 6(5): 630-641.
YANG ZE-SEN and TSE-SEN YANG. THE SU 2× SU 2BASIS AND THE PHYSICAL BASES FOR THE STATE VECTORS OF d-BOSON SYSTEMS AND THE TRACELESS BOSON OPERATORS (Ⅰ)[J]. Chinese Physics C, 1982, 6(5): 630-641. shu
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Received: 1982-03-04
Revised: 1900-01-01
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    THESU2×SU2BASIS AND THE PHYSICAL BASES FOR THE STATE VECTORS OF d-BOSON SYSTEMS AND THE TRACELESS BOSON OPERATORS (Ⅰ)

    • Department of Physics, Peking University
    • Received Date:1982-03-04
    • Accepted Date:1900-01-01
    • Available Online:1982-10-05

      Abstract:The group chainU5O5SU2×SU2used by K. T. Hecht (1965) and by the othersprovides an important representation for expressing the physical basis of d-boson sys-tems. However the methods which have been introduced for thisSU2×SU2representa-tion to construct a physical basis is poorer in comparison with those for the otherrepresentations. In view of this we try to find appropriate methods to obtain theSU2×SU2representation wave functions of the existing physical bases constructed byChacon et al. and by Szpikowski et al., In the present paper we analyse theSU2×SU2tensor properties of the,bosonoperators and Vilenkin's traceless boson operators and express succinctly the elementaryvectors of theSU2×SU2basis, the |PPSU2×SU2> vectors, in terms of the tracelessoperators. With the help of this form of the| PP SU2SU2> vectors we derive a simpleformula for obtaining theSU2×SU2-representation wave functions of a physical basisfrom its (nμ)-representation wave functions. Thus the problem mentioned above is partlysolved. The other parts of the solution of the problem will be found in a coming paper.

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