Exceptional parafermions in a Hilbert space over an associative algebra

  • L. C. Biedenharn
  • L. P. Horwitz
Contributed Papers I. Supersymmetry, Symmetry in Particle and Relativistic Physics
Part of the Lecture Notes in Physics book series (LNP, volume 79)


Hilbert Space Associative Algebra Clifford Algebra Linear Manifold Superselection Rule 
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  1. 1.
    H.H. Goldstine and L.P. Horwitz, Proc. Nat. Aca. Sci. 48, 1134 (1962); Math. Ann. 154, 1 (1964). For recent interest, see F. Gürsey, Orbis Scientiae Conference at Coral Gables, Jan. 1976, and references therein. See also, A. Barducci, F. Buccella, R.Casalbuoni, L. Lusanna and E. Sorace, Firenze preprint; Jan. 1977, where the isomorphism between the Jordan products of the Fermion operators of C6 and of the six transverse split octonions is noted. The authors were not interested in the non-observability aspects (presumably related to non-associativity), and therefore the associative realization was chosen and the automorphism groups of some of the Clifford algebras were studied. We emphasize in what follows that the non-associative aspects are implicit in the Clifford algebras, and hence the study carried out by Barducci et al. is actually of greater generality.Google Scholar
  2. 2.
    H.H. Goldstine and L.P. Horwitz, Math. Ann. 164, 291 (1966).Google Scholar
  3. 3.
    L.P. Horwitz and L.C. Biedenharn, Helv. Phys. Acta 38, 385 (1965).Google Scholar
  4. 4.
    M. Günaydin and F. Gürsey, Jour. Math. Phys. 14, 1651 (1973); Phys. Rev. D9, 3387 (1974); M. Günaydin, Jour. Math. Phys. 17, 1875 (1976).Google Scholar
  5. 5.
    See, for example, the representations of automorphism groups given by C. Saclioglu, Phys. Rev., in press.Google Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • L. C. Biedenharn
    • 1
  • L. P. Horwitz
    • 2
  1. 1.Duke UniversityDurhamUSA
  2. 2.Tel Aviv UniversityRamat AvivIsrael

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