THE IMPACT OF GIULIO RACAH ON CRYSTAL- AND LIGAND-FIELD THEORIES

Abstract : 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.
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Conference papers
Rutwig Campoamor-Stursberg and Luis J. Boya. International Conference in Commemoration of the Centenary of the Birth of G. Racah (1909-1965) - Zaragoza, Spain, 22-24 February 2010, Feb 2010, Zaragoza, Spain. 37, pp.37-84


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Contributor : Maurice Robert Kibler <>
Submitted on : Friday, March 11, 2011 - 2:00:53 PM
Last modification on : Friday, January 6, 2012 - 6:00:33 PM

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  • HAL Id : in2p3-00575948, version 1
  • ARXIV : 1103.2272

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Maurice Robert Kibler. THE IMPACT OF GIULIO RACAH ON CRYSTAL- AND LIGAND-FIELD THEORIES. Rutwig Campoamor-Stursberg and Luis J. Boya. International Conference in Commemoration of the Centenary of the Birth of G. Racah (1909-1965) - Zaragoza, Spain, 22-24 February 2010, Feb 2010, Zaragoza, Spain. 37, pp.37-84. <in2p3-00575948>

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