Vector coherent state theory of the generic representations of so(5) in an so(3) basis

Details Vector coherent state theory of the generic representations of so(5) in an so(3) basis Vector coherent state theory of the generic representations of so(5) in an so(3) basis

2005-11-15

arxiv.org/abs/math-ph/0511052v1

J.Math.Phys. 47 (2006) 023507

Physics

Mathematical Physics

20 pages, uses multirow.sty, submitted to J. Math. Phys

Scientific paper

10.1063/1.2162332

For applications of group theory in quantum mechanics, one generally needs explicit matrix representations of the spectrum generating algebras that arise in bases that reduce the symmetry group of some Hamiltonian of interest. Here we use vector coherent state techniques to develop an algorithm for constructing the matrices for arbitrary finite-dimensional irreps of the SO(5) Lie algebra in an SO(3) basis. The SO(3) subgroup of SO(5) is defined by regarding SO(5) as linear transformations of the five-dimensional space of an SO(3) irrep of angular momentum two. A need for such irreps arises in the nuclear collective model of quadrupole vibrations and rotations. The algorithm has been implemented in MAPLE, and some tables of results are presented.

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