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Resolution of the GL(3) O(3) state labelling problem via the O(3)-invariant Bethe subalgebra of the twisted Yangain

Citation

Jarvis, PD and Zhang, RB, Resolution of the GL(3) O(3) state labelling problem via the O(3)-invariant Bethe subalgebra of the twisted Yangain, Journal of Physics A: Mathematical and General, 38, (14) pp. L219-L226. ISSN 0305-4470 (2005) [Refereed Article]

DOI: doi:10.1088/0305-4470/38/14/L03

Abstract

The labelling of states of irreducible representations of GL(3) in an O(3) basis is well known to require the addition of a single O(3)-invariant operator, to the standard diagonalizable set of Casimir operators in the subgroup chain GL(3) ⊃ O(3) ⊃ O(2). Moreover, this 'missing label' operator must be a function of the two independent cubic and quartic invariants which can be constructed in terms of the angular momentum vector and the quadrupole tensor. It is pointed out that there is a unique (in a well-defined sense) combination of these which belongs to the O(3)-invariant Bethe subalgebra of the twisted Yangian Y(GL(3); O(3)) in the enveloping algebra of GL(3). © 2005 IOP Publishing Ltd.

Item Details

Item Type:Refereed Article
Research Division:Physical Sciences
Research Group:Other Physical Sciences
Research Field:Physical Sciences not elsewhere classified
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Physical Sciences
Author:Jarvis, PD (Dr Peter Jarvis)
ID Code:36495
Year Published:2005
Funding Support:Australian Research Council (DP0208808)
Web of Science® Times Cited:6
Deposited By:Physics
Deposited On:2005-08-01
Last Modified:2006-03-29
Downloads:0

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