Broken Unitary Tableaus, Itinerant Nuclear Spins, and Spontaneous Molecular Symmetry Collapse

  • Willian G. Harter
  • Chris W. Patterson
Part of the Lecture Notes in Chemistry book series (LNC, volume 22)


Applications of unitary group (Um) and permutation group (Sn) representations have been the subject of two conferences organized by Professor Jürgen Hinze. The proceedings of the present conference mostly emphasize applications of unitary groups, while the those of the preceeding conference (1) mostly emphasize the permutation groups. A number of papers notably those of Wormer and Sarma in this volume, have reminded us of the inescapable relations between Um and Sn groups. Many of the papers in these volumes have dealt with some number n of indistinguishable spin − 1/2 particles, for example, orbiting electrons, which may occupy some other number m of distinguishable states. The permutation group Sn of distinguishable particles serves as a symmetry group for the system Hamiltonian. The unitary group Um corresponds to the set of all superpositions of the m states which preserve quantum amplitudes. The group Um will be a symmetry group only if the m states remain degenerate in energy. Nevertheless, the Um operations always commute with the Sn permutations so in some sense the two groups are symmetries for each other.


Angular Momentum Nuclear Spin Unitary Group Cluster State Permutation Group 
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Copyright information

© Springer-Verlag Berlin · Heidelberg 1981

Authors and Affiliations

  • Willian G. Harter
    • 1
  • Chris W. Patterson
    • 2
  1. 1.School of PhysicsGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Los Alamos Scientific LaboratoryLos AlamosMexico

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