Time Reversal and Nonunitary Groups

Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 78)


When the system under consideration is invariant with respect to time reversal, it is possible to regard it as having the symmetry of a nonunitary group which consists of time reversal θ in addition to the unitary symmetry operations considered so far. The purpose of this chapter is to discuss the representations (corepresentations) of such nonunitary groups and to examine the additional degeneracy brought in by including the operation θ. A well-known example of a nonunitary group is the magnetic space group. By considering this group, the symmetry of magnons (spin waves) and excitons in magnetic compounds and selection rules for their excitation can be treated in the same way as excitons in molecular crystals.


Irreducible Representation Time Reversal Irreducible Character Symmetry Operation Magnetic Compound 
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  1. 13.1
    R. E. Dietz, A. Misetich, H. J. Guggenheim: Phys. Rev. Lett. 16, 841 (1966)ADSCrossRefGoogle Scholar
  2. 13.2
    Tables of the irreducible characters are due to J. O. Dimmock, R. G. Wheeler: Phys. Rev. 127, 391 (1962)MathSciNetADSzbMATHCrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  1. 1.Japan Women’s UniversityBunkyo-ku, Tokyo 112Japan
  2. 2.Department of Physics, School of Science and TechnologyMeiji UniversityTama-ku, Kawasaki 214Japan

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