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World spinors—Construction and some applications

  • Part II. Invited Papers Dedicated to Lawrence Biedenharn
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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.

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References

  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. Y. Dothan, M. Gell-Mann, and Y. Ne'eman,Phys. Lett. 17, 148 (1965).

    Article  ADS  MathSciNet  Google Scholar 

  3. Dj. Šijački and Y. Ne'eman,Phys. Lett. B 247, 571 (1990).

    Article  ADS  Google Scholar 

  4. J. P. Elliott,Proc. R. Soc. London A,245, 128, 562 (1958).

    Article  ADS  Google Scholar 

  5. L. Weaver and L. C. Biedenharn,Phys. Lett. B 32, 326 (1970).

    Article  ADS  Google Scholar 

  6. J. P. Draayer and K. J. Weeks,Phys. Rev. Lett. 51, 1422 (1983).

    Article  ADS  Google Scholar 

  7. D. W. Joseph, University of Nebraska, preprint (unpublished), 1969.

  8. V. I. Ogievetsky and E. Sokatchev,Teor. Mat. Fiz. 23, 462 (1975).

    Google Scholar 

  9. Dj. Šijački,J. Math. Phys. 16, 298 (1975).

    Article  MATH  Google Scholar 

  10. B. Speh,Math. Ann. 258, 113 (1981).

    Article  MathSciNet  MATH  Google Scholar 

  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. Y. Ne'eman,Proc. Natl. Acad. Sci. USA,74, 415 (1977).

    Article  Google Scholar 

  13. Y. Ne'eman,Ann. Inst. H. Poincaré A 28, 369 (1978).

    MathSciNet  MATH  Google Scholar 

  14. Y. Ne'eman and Dj. Šijački,Phys. Lett. B 157, 267 (1985).

    Article  ADS  MathSciNet  Google Scholar 

  15. V. I. Ogievetsky and I. V. Polubarinov,Sov. Phys. JETP,21, 1093 (1965).

    ADS  Google Scholar 

  16. F. W. Hehl, G. D. Kerlick, and P. von der Heyde,Phys. Lett. B 63, 446 (1976).

    Article  ADS  MathSciNet  Google Scholar 

  17. Y. Ne'eman and Dj. Šijački,Ann. Phys. (N.Y.) 120, 292 (1979).

    Article  ADS  Google Scholar 

  18. F. W. Hehl, J. D. McCrea, E. W. Mielke, and Y. Ne'eman,Phys. Rep. 258, 1 (1995).

    Article  ADS  MathSciNet  Google Scholar 

  19. Dj. Šijački and Y. Ne'eman,J. Math. Phys. 26, 2475 (1985).

    Google Scholar 

  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. V. Bargmann,Ann. Math. 48, 568 (1947).

    Article  MathSciNet  Google Scholar 

  22. A. Cant and Y. Ne'eman,J. Math. Phys. 26, 3180 (1985).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. Dj. Šijački,Phys. Lett. B 109, 435 (1982).

    Article  MathSciNet  Google Scholar 

  24. Y. Ne'eman and Dj. Šijački,Phys. Lett. B,200, 489 (1988).

    Article  ADS  MathSciNet  Google Scholar 

  25. Y. Ne'eman and Dj. Šijački,Phys. Rev. D 37, 3267 (1988).

    Article  ADS  MathSciNet  Google Scholar 

  26. Dj. Šijački and Y. Ne'eman,Phys. Rev. D 47, 4133 (1993).

    Article  ADS  Google Scholar 

  27. S. Helgason,Differential Geometry and Symmetric Spaces (Academic, New York, 1982).

    Google Scholar 

  28. T. E. Stewart,Proc. Am. Math. Soc. 11, 559 (1960).

    Article  MATH  Google Scholar 

  29. N. Miljkovic, M.Sc. Thesis, Belgrade University, 1987.

  30. J. Mickelsson,Commun. Math. Phys. 88, 551 (1983).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  31. A. B. Borisov,J. Phys. 11, 1057 (1978).

    Article  MathSciNet  ADS  Google Scholar 

  32. E. Eizenberg and Y. Ne'eman,Membranes and Other Extendons (World Scientific, Singapore, 1995).

    Google Scholar 

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Author notes

  1. Yuval Ne'eman (Wolfson Distinguished Chair in Theoretical Physics)

    Present address: Center for Particle Physics, University of Texas, 78712, Austin, Texas, USA

Authors and Affiliations

  1. Sackler Faculty of Exact Sciences, Tel-Aviv University, 69978, Tel-Aviv, Israel

    Yuval Ne'eman (Wolfson Distinguished Chair in Theoretical Physics)

  2. Institute of Physics, P.O. Box 57, Belgrade, Yugoslavia

    Djordje Šijački

Authors
  1. Yuval Ne'eman
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  2. Djordje Šijački
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Supported in part by the Science Foundation (Belgrade).

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Ne'eman, Y., Šijački, D. World spinors—Construction and some applications. Found Phys 27, 1105–1122 (1997). https://doi.org/10.1007/BF02551436

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  • DOI: https://doi.org/10.1007/BF02551436

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