David J Siminovitch and Simon Habot 1997 J. Phys. A: Math. Gen. 30 2577 doi:10.1088/0305-4470/30/7/033
David J Siminovitch and Simon Habot
Show affiliationsA disentanglement of the rotation operator introduced by Santiago and Vaidya is used to prove the composition rule for the Euler - Rodrigues parameters in a representation-independent manner. It is also shown that one of the Santiago and Vaidya disentangling coefficients embodies the Darboux transformation of differential geometry, which is equivalent to stereographic projection of the Bloch sphere onto the complex plane.
02.40.-k Geometry, differential geometry, and topology
02.20.Qs General properties, structure, and representation of Lie groups
Issue 7 (7 April 1997)
Received 14 October 1996
David J Siminovitch and Simon Habot 1997 J. Phys. A: Math. Gen. 30 2577
S G Schirmer et al 2004 J. Phys. A: Math. Gen. 37 1389
J T Lin and T F Jiang 2000 J. Phys. B: At. Mol. Opt. Phys. 33 3023
J C Camparo and R P Frueholz 1984 J. Phys. B: At. Mol. Phys. 17 4169
Witold Chałupczak and Krzysztof Szymaniec 2006 J. Phys. B: At. Mol. Opt. Phys. 39 1081
Bogdan A Bernevig and Han-Dong Chen 2003 J. Phys. A: Math. Gen. 36 8325
A Karpati and Z Kis 2003 J. Phys. B: At. Mol. Opt. Phys. 36 905
Luís E E de Araujo and Ian A Walmsley 2003 J. Opt. B: Quantum Semiclass. Opt. 5 R27
Marco Frasca 2001 J. Opt. B: Quantum Semiclass. Opt. 3 S15
Yutaka Okabe and Hiromi Otsuka 2006 J. Phys. A: Math. Gen. 39 9093