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

Article

1-1-2014

## Abstract

A recursive method for the construction of symmetric irreducible representations of (Formula Presented.) in the (Formula Presented.) basis for identical boson systems is proposed. The formalism is realized based on the group chain (Formula Presented.) , of which the symmetric irreducible representations are simply reducible. The basis vectors for symmetric irreducible representations of the (Formula Presented.) can easily be constructed from those of U(2l + 1) (Formula Presented.)U(2l - 1) ⊗ U(2) (Formula Presented.)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 (Formula Presented.) in the (Formula Presented.) 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 (Formula Presented.) basis, where (Formula Presented.) , 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 (Formula Presented.) (Formula Presented.) with (Formula Presented.) , 0, -1. Matrix representations of (Formula Presented.) , together with the elementary Wigner coefficients, are presented. After the angular momentum projection, a three-term relation in determining the expansion coefficients of the (Formula Presented.) basis vectors, where the O(3) group is generated by the angular momentum operators of the d -boson system, in terms of those of (Formula Presented.) is derived. The eigenvectors of the projection matrix with zero eigenvalues constructed according to the three-term relation completely determine the basis vectors of (Formula Presented.). Formulae for evaluating the elementary Wigner coefficients of (Formula Presented.) are derived explicitly. Analytical expressions of some elementary Wigner coefficients of (Formula Presented.) for the coupling (Formula Presented.) with resultant angular momentum quantum number L = 2(Formula Presented.) + 2 - k for (Formula Presented.) with a multiplicity 2 case for k = 6 are presented.

## Publication Source (Journal or Book title)

European Physical Journal Plus

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