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

TL;DR

This paper develops an algorithm using vector coherent states to explicitly construct matrix representations of SO(5) irreducible representations in an SO(3) basis, aiding nuclear physics models.

Contribution

It introduces a novel algorithm for constructing SO(5) irreps in an SO(3) basis using vector coherent states, implemented in MAPLE.

Findings

Algorithm successfully constructs matrices for SO(5) irreps.

Implementation in MAPLE facilitates practical computations.

Results include tables of explicit matrix representations.

Abstract

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.