Clebsch-Gordan Coefficients for SL(n, C)

The Clebsch–Gordan coefficients for the coupling of certain degenerate representations of SL(n, C) are expressed as generalized hypergeometric functions. These coefficients define the baryon ‘current’ which is coupled to the lowest state of a meson tower in the SL(6, C) theory of elementary particle...

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Bibliographic Details
Published in:Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences Mathematical and physical sciences, 1967-09, Vol.300 (1462), p.337-355
Main Author: Bamberg, P. G
Format: Article
Language:English
Subjects:
Baryons
Coefficients
Coupling coefficients
Hypergeometric functions
Integers
Mesons
Orthogonality
Recurrence relations
Series convergence
Tensors
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Summary:The Clebsch–Gordan coefficients for the coupling of certain degenerate representations of SL(n, C) are expressed as generalized hypergeometric functions. These coefficients define the baryon ‘current’ which is coupled to the lowest state of a meson tower in the SL(6, C) theory of elementary particles. The asymptotic behaviour of the coefficients for high states in the baryon tower is determined. Orthogonality and completeness relations are proved which lead to an explicit formula for decomposing a two-particle state into a direct integral of ‘currents ’ which belong to the principal series of meson representations. The relation between SL(n, C) Clebsch–Gordan coefficients and SU(n) 9–j symbols is explored.
ISSN:1364-5021
0080-4630
1471-2946
2053-9169
DOI:10.1098/rspa.1967.0174