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THE IMPACT OF GIULIO RACAH ON CRYSTAL- AND LIGAND-FIELD THEORIES
Kibler M. R.
Dans Monografias de la Real Academia de Ciencias de Zaragoza - International Conference in Commemoration of the Centenary of the Birth of G. Racah (1909-1965) - Zaragoza, Spain, 22-24 February 2010, Zaragoza : Espagne (2010) - http://hal.in2p3.fr/in2p3-00575948
Physique/Physique Quantique
Sciences de l'Homme et Société/Histoire, Philosophie et Sociologie des sciences
Physique/Matière Condensée/Autre
Physique/Physique/Agrégats Moléculaires et Atomiques
THE IMPACT OF GIULIO RACAH ON CRYSTAL- AND LIGAND-FIELD THEORIES
Maurice Robert Kibler ()1
1 :  IPNL - Institut de Physique Nucléaire de Lyon
http://www.ipnl.in2p3.fr/
CNRS : UMR5822 – IN2P3 – Université Claude Bernard - Lyon I (UCBL)
France
This paper focuses on the impact of Racah on crystal- and ligand-field theories, two branches of molecular physics and condensed matter physics (dealing with ions embedded in aggregates of finite symmetry). The role of Racah and some of his students in developing a symmetry-adapted weak-field model for crystal-field theory is examined. Then, we discuss the extension of this model to a generalized symmetry-adapted weak-field model for ligand-field theory. Symmetry considerations via the use of the Wigner-Racah algebra for chains of type SU(2) > G is essential for these weak-field models. Therefore, the basic ingredients for the Wigner-Racah algebra of a finite or compact group are reviewed with a special attention paid to the SU(2) group in a SU(2) > G basis. Finally, as an unexpected application of nonstandard SU(2) bases, it is shown how SU(2) bases adapted to the cyclic group allow to build bases of relevance in quantum information.

Communications avec actes
2011
24/02/2010
Monografias de la Real Academia de Ciencias de Zaragoza
internationale
37
Rutwig Campoamor-Stursberg and Luis J. Boya
37-84

International Conference in Commemoration of the Centenary of the Birth of G. Racah (1909-1965) - Zaragoza, Spain, 22-24 February 2010
Zaragoza
Espagne
21/02/2010
24/02/2010
M.R. Kibler

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