The Clebsch-Gordan coefficients of SU(3) and the orthogonalization problem
The Clebsch-Gordan coefficients of the group SU(3) are determined by integrating the product of three matrix elements of finite transformations belonging to three irreducible representations of the group. Compact expressions involving a single or a double sum over products of 3-j and 6-j symbols of SU(2) are obtained for several different classes of coefficients by suitably restructing the initial states but keeping the final states of the matrix elements arbitrary. To orthogonalize the CG coefficients, a linear combination of several integrals with the same final but different initial states is taken. The coefficients of the linear combination are determined by the Schmidt procedure and are found to be expressible in terms of integrals of the same type.
- Research Organization:
- Department of Physics, Indian Institute of Technology, Kharagpur, India
- Sponsoring Organization:
- USDOE
- NSA Number:
- NSA-29-004392
- OSTI ID:
- 4396562
- Journal Information:
- Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 9 Vol. 14; ISSN 0022-2488
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
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