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Foundations of Physics

, Volume 27, Issue 8, pp 1105–1122 | Cite as

World spinors—Construction and some applications

  • Yuval Ne'eman
  • Djordje Šijački
Part II. Invited Papers Dedicated to Lawrence Biedenharn

Abstract

The existence of a topological double-covering for the GL(n, R) and diffeomorphism groups is reviewed. These groups do not have finite-dimensional faithful representations. An explicit construction and the classification of all\(\overline {SL} \)(n, R), n=3,4 unitary irreducible representations is presented. Infinite-component spinorial and tensorial\(\overline {SL} \) fields, “manifields”, are introduced. Particle content of the ladder manifields, as given by the\(\overline {SL} \)(3, R) “little” group, is determined. The manifields are lifted to the corresponding world spinorial and tensorial manifields by making use of generalized infinite-component frame fields. World manifields transform w.r.t. corresponding\(\overline {Diff} \) representations, which are constructed explicitly.

Keywords

Invariant Subspace Unitary Representation Compact Subgroup Spinorial Representation Maximal Compact Subgroup 
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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References

  1. 1.
    L. C. Biedenharn, M. A. Locke, and J. D. Louck. “The canonical resolution of the multiplicity problem forSU(3)” inProceedings, 4th International Colloquim on Group-Theoretical Methods in Physics, Nijmegen, The Netherlands, 1975, A. Janner, T. Janssen, and M. Boon, eds., Springer Verlag, Lecture Notes in Physics, Vol. 50 (Berlin, Heidelberg, New York, 1976), pp. 395–403.Google Scholar
  2. 2.
    Y. Dothan, M. Gell-Mann, and Y. Ne'eman,Phys. Lett. 17, 148 (1965).CrossRefADSMathSciNetGoogle Scholar
  3. 3.
    Dj. Šijački and Y. Ne'eman,Phys. Lett. B 247, 571 (1990).CrossRefADSGoogle Scholar
  4. 4.
    J. P. Elliott,Proc. R. Soc. London A,245, 128, 562 (1958).ADSCrossRefGoogle Scholar
  5. 5.
    L. Weaver and L. C. Biedenharn,Phys. Lett. B 32, 326 (1970).CrossRefADSGoogle Scholar
  6. 6.
    J. P. Draayer and K. J. Weeks,Phys. Rev. Lett. 51, 1422 (1983).CrossRefADSGoogle Scholar
  7. 7.
    D. W. Joseph, University of Nebraska, preprint (unpublished), 1969.Google Scholar
  8. 8.
    V. I. Ogievetsky and E. Sokatchev,Teor. Mat. Fiz. 23, 462 (1975).Google Scholar
  9. 9.
    Dj. Šijački,J. Math. Phys. 16, 298 (1975).CrossRefzbMATHGoogle Scholar
  10. 10.
    B. Speh,Math. Ann. 258, 113 (1981).CrossRefMathSciNetzbMATHGoogle Scholar
  11. 11.
    Y. Ne'eman, inGR8 (Proc. 8th Int. Conf. on Gen. Relativ. and Gravit.), M. A. McKiernan, ed. (University of Waterloo, Waterloo, Canada, 1977), p. 269.Google Scholar
  12. 12.
    Y. Ne'eman,Proc. Natl. Acad. Sci. USA,74, 415 (1977).CrossRefGoogle Scholar
  13. 13.
    Y. Ne'eman,Ann. Inst. H. Poincaré A 28, 369 (1978).MathSciNetzbMATHGoogle Scholar
  14. 14.
    Y. Ne'eman and Dj. Šijački,Phys. Lett. B 157, 267 (1985).CrossRefADSMathSciNetGoogle Scholar
  15. 15.
    V. I. Ogievetsky and I. V. Polubarinov,Sov. Phys. JETP,21, 1093 (1965).ADSGoogle Scholar
  16. 16.
    F. W. Hehl, G. D. Kerlick, and P. von der Heyde,Phys. Lett. B 63, 446 (1976).CrossRefADSMathSciNetGoogle Scholar
  17. 17.
    Y. Ne'eman and Dj. Šijački,Ann. Phys. (N.Y.) 120, 292 (1979).CrossRefADSGoogle Scholar
  18. 18.
    F. W. Hehl, J. D. McCrea, E. W. Mielke, and Y. Ne'eman,Phys. Rep. 258, 1 (1995).CrossRefADSMathSciNetGoogle Scholar
  19. 19.
    Dj. Šijački and Y. Ne'eman,J. Math. Phys. 26, 2475 (1985).Google Scholar
  20. 20.
    Dj. Šijački, “\(\overline {SL} \)(n, R) spinors for particles, gravity and superstrings”, inSpinors in Physics and Geometry, A. Trautman and G. Furlan, eds. (World Scientific, Singapore, 1988), pp. 191–206.Google Scholar
  21. 21.
    V. Bargmann,Ann. Math. 48, 568 (1947).CrossRefMathSciNetGoogle Scholar
  22. 22.
    A. Cant and Y. Ne'eman,J. Math. Phys. 26, 3180 (1985).CrossRefADSMathSciNetzbMATHGoogle Scholar
  23. 23.
    Dj. Šijački,Phys. Lett. B 109, 435 (1982).CrossRefMathSciNetGoogle Scholar
  24. 24.
    Y. Ne'eman and Dj. Šijački,Phys. Lett. B,200, 489 (1988).CrossRefADSMathSciNetGoogle Scholar
  25. 25.
    Y. Ne'eman and Dj. Šijački,Phys. Rev. D 37, 3267 (1988).CrossRefADSMathSciNetGoogle Scholar
  26. 26.
    Dj. Šijački and Y. Ne'eman,Phys. Rev. D 47, 4133 (1993).CrossRefADSGoogle Scholar
  27. 27.
    S. Helgason,Differential Geometry and Symmetric Spaces (Academic, New York, 1982).Google Scholar
  28. 28.
    T. E. Stewart,Proc. Am. Math. Soc. 11, 559 (1960).CrossRefzbMATHGoogle Scholar
  29. 29.
    N. Miljkovic, M.Sc. Thesis, Belgrade University, 1987.Google Scholar
  30. 30.
    J. Mickelsson,Commun. Math. Phys. 88, 551 (1983).CrossRefADSMathSciNetzbMATHGoogle Scholar
  31. 31.
    A. B. Borisov,J. Phys. 11, 1057 (1978).CrossRefMathSciNetADSGoogle Scholar
  32. 32.
    E. Eizenberg and Y. Ne'eman,Membranes and Other Extendons (World Scientific, Singapore, 1995).Google Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • Yuval Ne'eman
    • 1
  • Djordje Šijački
    • 2
  1. 1.Sackler Faculty of Exact SciencesTel-Aviv UniversityTel-AvivIsrael
  2. 2.Institute of PhysicsBelgradeYugoslavia

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