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

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.

arXiv comment20 pages, uses multirow.sty, submitted to J. Math. Phys

References in corpus (3)

• An SU(4) Model of High-Temperature Superconductivity and Antiferromagnetism
• Vector coherent state representations, induced representations, and geometric quantization: I. Scalar coherent state representations
• Coherent state triplets and their inner products

Cited by in corpus (6)

• Quadrupole collective variables in the natural Cartan-Weyl basis
• Racah's method for general subalgebra chains: Coupling coefficients of SO(5) in canonical and physical bases
• The quadrupole collective model from a Cartan-Weyl perspective
• Spectral properties of a tractable collective Hamiltonian
• Obtainment of internal labelling operators as broken Casimir operators by means of contractions related to reduction chains in semisimple Lie algebras
• Noncommutative pfaffians and classification of states of five-dimensional quasi-spin