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Construction of Basis Vectors For Symmetric \Irreducible Representations of $O(5)supset O(3)$
Pan Feng 1 *,Bao Lina 1,Zhang Yaozhong 2,J P Draayer 3
1.Department of Physics，Liaoning Normal University，Dalian 116029
2.School of Mathematics and Physics,The University of Queesland,Brishane Qld 4072,Australia
3.Department of Physics and Astronomy, Louisiana State University, Baton Rouge,LA 70803-4001,USA
*Correspondence author
#Submitted by
Subject:
Funding: Natural Science Foundation of Liaoning Province （No.2013020091）, U.S. National Science Foundation （No.OCI-0904874）, Australian Research Council（No.DP110103434）, Doctoral Program Foundation of the State Education Ministryof China (20102136110002)��Natural Science Foundation of China （No.11175078; 11375080）
Opened online:29 September 2013
Accepted by: none
Citation: Pan Feng,Bao Lina,Zhang Yaozhong.Construction of Basis Vectors For Symmetric \Irreducible Representations of $O(5)supset O(3)$[OL]. [29 September 2013] http://en.paper.edu.cn/en_releasepaper/content/4560983
 
 
A recursive method for construction of symmetric irreducible representationsof $O(2l+1)$ in the $O(3)$ basis for identical boson systems is proposed.As a starting point, basis vectors of symmetric irreducible representations of $O(5)$are constructed in the $O_{1}(3)otimes U(1)$ basis.Matrix representations of $O(5)supset O_{1}(3)otimes U(1)$, together withthe elementary Wigner coefficients, are presented.After the angular momentum projection, a three-term relation in determining the expansioncoefficients of the $O(5)supset O(3)$ basis vectors in terms of those ofthe $O_{1}(3)otimes U(1)$ is derived. The eigenvectorsof the projection matrix with zero eigenvalues constructed according to the three-term relationcompletely determine the basis vectors of$O(5)supset O(3)$. Formulae for evaluating theelementary Wigner coefficients of $O(5)$ $supset O(3)$ are derived explicitly.Analytical expressionsof some elementary Wigner coefficients of $O(5)supset$ $O(3)$for the coupling $( au~0)otimes (1~0)$ with resultantangular momentum quantum number $L=$ $2 au+2-k$ for$k=0,2,3,cdots,6$ with a multiplicity $2$ case for $k=6$ arepresented.
Keywords:Mathematical physics, symmetric irreps, angular momentum projection, Wigner coefficients
 
 
 

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