THE SU2×SU2 BASIS AND THE PHYSICAL BASES FOR THE STATE VECTORS OF d-BOSON SYSTEMS AND THE TRACELESS BOSON OPERATORS (Ⅰ)

YANG ZE-SEN; TSE-SEN YANG

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2024年10月30日

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

THE SU₂×SU₂BASIS AND THE PHYSICAL BASES FOR THE STATE VECTORS OF d-BOSON SYSTEMS AND THE TRACELESS BOSON OPERATORS (Ⅰ)

Department of Physics, Peking University

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Abstract：
The group chain U₅O₅SU₂×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 this SU₂×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 the SU₂×SU₂representation wave functions of the existing physical bases constructed byChacon et al. and by Szpikowski et al., In the present paper we analyse the SU₂×SU₂tensor properties of the,bosonoperators and Vilenkin's traceless boson operators and express succinctly the elementaryvectors of the SU₂×SU₂basis, the |PP SU₂×SU₂> vectors, in terms of the tracelessoperators. With the help of this form of the| PP SU₂ SU₂> vectors we derive a simpleformula for obtaining the SU₂×SU₂-representation wave functions of a physical basisfrom its (n_μ)-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.

References

[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 SU₂×SU₂BASIS 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 SU₂×SU₂BASIS 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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沈阳化工大学材料科学与工程学院沈阳 110142

THE SU₂×SU₂BASIS AND THE PHYSICAL BASES FOR THE STATE VECTORS OF d-BOSON SYSTEMS AND THE TRACELESS BOSON OPERATORS (Ⅰ)

YANG ZE-SEN
TSE-SEN YANG

Department of Physics, Peking University

Received Date: 1982-03-04
Accepted Date: 1900-01-01
Available Online: 1982-10-05

Abstract: The group chain U₅O₅SU₂×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 this SU₂×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 the SU₂×SU₂representation wave functions of the existing physical bases constructed byChacon et al. and by Szpikowski et al., In the present paper we analyse the SU₂×SU₂tensor properties of the,bosonoperators and Vilenkin's traceless boson operators and express succinctly the elementaryvectors of the SU₂×SU₂basis, the |PP SU₂×SU₂> vectors, in terms of the tracelessoperators. With the help of this form of the| PP SU₂ SU₂> vectors we derive a simpleformula for obtaining the SU₂×SU₂-representation wave functions of a physical basisfrom its (n_μ)-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.