THE IMPACT OF GIULIO RACAH ON CRYSTAL- AND LIGAND-FIELD THEORIES - IN2P3 - Institut national de physique nucléaire et de physique des particules Access content directly
Conference Papers Year : 2011

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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Dates and versions

in2p3-00575948 , version 1 (11-03-2011)

Identifiers

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

Cite

Maurice Robert Kibler. THE IMPACT OF GIULIO RACAH ON CRYSTAL- AND LIGAND-FIELD THEORIES. 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. pp.37-84. ⟨in2p3-00575948⟩
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