Systems, Subsystems and Induced Representations

  • D. J. Newman

Abstract

In conventional (Racah) state labelling schemes a sequence of groups G ⊃ ... ⊃ H is employed, where G is a covering group in which the physical bases are uniquely labelled by irreducible representations, or irreps, and H is the symmetry group of the system. Intermediate groups in the sequence are chosen to ensure that the irreps of H spanned by the physical bases are uniquely specified. This makes it possible to use standard group theoretical techniques to determine matrix elements for complex systems. In some cases of interest, however, sequences which satisfy these criteria do not exist (e.g. relating R3 to the octahedral group). We are then forced to look at induction techniques. Even when we are not forced it may, nevertheless, be preferable to use induced representations for labelling because of the better insight they provide into the structure of the physical eigenstates.

Keywords

Brillouin Zone Octahedral Group Cyclic Region Cyclic Boundary Condition Coset Decomposition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1986

Authors and Affiliations

  • D. J. Newman
    • 1
  1. 1.Department of PhysicsUniversity of Hong KongHong Kong

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