A new procedure for constructing basis vectors of irreducible representations of SU(3) under the $$ SU(3) \supset SO(3) $$ basis

Feng Pan (), K. D. Launey () and J. P. Draayer ()
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Feng Pan: Liaoning Normal University, Department of Physics
K. D. Launey: Louisiana State University, Department of Physics and Astronomy
J. P. Draayer: Louisiana State University, Department of Physics and Astronomy

A chapter in Physical and Mathematical Aspects of Symmetries, 2017, pp 287-292 from Springer

Abstract: Abstract An effective algebraic angular momentum projection procedure for constructing basis vectors of an irreducible representation of the Lie group SU(3) under the non-canonical $$ SU(3) \supset SO(3) \supset SO(2) $$ basis from those of the canonical $$ U(2) \supset U(1) $$ basis is outlined. The expansion coefficients are components of the nullspace vectors of a projection matrix with, in general, four nonzero elements in each row, where the projection matrix is derived from known matrix elements of the U(3) generators in the canonical basis. The advantage of the new procedure lies in the fact that the Hill-Wheeler integral involved in Elliott’s projection operator method used previously is avoided, thereby achieving faster numerical calculations with improved accuracy. However, the Gram-Schmidt orthonormalization is still needed in order to provide orthonormalized basis vectors.

Date: 2017
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DOI: 10.1007/978-3-319-69164-0_42

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