# Construction of basis vectors for symmetric irreducible representations of O(5) (Formula Presented.) O(3)

Pan, Feng, Bao, Lina, Zhang, Yao-Zhong and Draayer, Jerry P. (2014) Construction of basis vectors for symmetric irreducible representations of O(5) (Formula Presented.) O(3). European Physical Journal Plus, 129 8: 1-27. doi:10.1140/epjp/i2014-14169-0

Author Pan, FengBao, LinaZhang, Yao-ZhongDraayer, Jerry P. Construction of basis vectors for symmetric irreducible representations of O(5) (Formula Presented.) O(3) Construction of basis vectors for symmetric irreducible representations of O(5) ⊃ O(3) European Physical Journal Plus   Check publisher's open access policy 2190-5444 2014-08 2014 Article (original research) 10.1140/epjp/i2014-14169-0 129 8 1 27 27 Heidelberg, Germany Springer 2015 eng A recursive method for the construction of symmetric irreducible representations of O(2l+1) in the O(2l+1)⊃O(3) basis for identical boson systems is proposed. The formalism is realized based on the group chain U(2l+1)⊃U(2l−1)⊗U(2) , of which the symmetric irreducible representations are simply reducible. The basis vectors for symmetric irreducible representations of the O(2l+1)⊃O(2l−1)⊗U(1) can easily be constructed from those of U(2l + 1) ⊃ U(2l - 1) ⊗ U(2) ⊃ O(2l - 1) ⊗ U(1) with no l -boson pairs, namely with the total boson number exactly equal to the seniority number in the system, from which one can construct symmetric irreducible representations of O(2l+1) in the O(2l−1)⊗U(1) basis when all symmetric irreducible representations of O(2l - 1) are known. As a starting point, basis vectors of symmetric irreducible representations of O(5) are constructed in the O1(3)⊗U(1) basis, where O1(3)≡O(2l−1) , when l = 2 , which is generated not by the angular momentum operators of the d -boson system, but by the operators constructed from d -boson creation (annihilation) operators d†μ ( dμ with μ=1 , 0, -1 . Matrix representations of O(5)⊃O1(3)⊗U(1) , together with the elementary Wigner coefficients, are presented. After the angular momentum projection, a three-term relation in determining the expansion coefficients of the O(5)⊃O(3) basis vectors, where the O(3) group is generated by the angular momentum operators of the d -boson system, in terms of those of O1(3)⊗U(1) is derived. The eigenvectors of the projection matrix with zero eigenvalues constructed according to the three-term relation completely determine the basis vectors of O(5)⊃O(3) . Formulae for evaluating the elementary Wigner coefficients of O(5)⊃O(3) are derived explicitly. Analytical expressions of some elementary Wigner coefficients of O(5)⊃O(3) for the coupling (τ0)⊗(10) with resultant angular momentum quantum number L = 2 τ + 2 - k for k=0,2,3,…,6 with a multiplicity 2 case for k = 6 are presented. C1 Confirmed Code UQ

 Document type: Journal Article Article (original research) School of Mathematics and Physics Official 2015 Collection

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