Skip to main content
SpringerLink
Log in

Quaternionic and supersymmetric σ — models

  • Part I Proceedings Of The International Colloquium Of The C.N.R.S. Held At Aix-en-Provence, September 3–7, 1979 Edited By J.M. Souriau
  • Conference paper
  • First Online:
Differential Geometrical Methods in Mathematical Physics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 836))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. Helgason, "Differential geometry and symmetric spaces", Academic Press, New York, 1962

    MATH  Google Scholar 

  2. S. Kobayashi and K. Nom zu, "Foundations of Differential Geometry", Vol. II, Interscience Publ. New York, 1968

    Google Scholar 

  3. A.A. Slavnov, TMF 10, 305 /1972/

    Google Scholar 

  4. F. Gürsey and L. Marchildon, Phys.Rev. D 17, 2038 /1978/

    Google Scholar 

  5. I.J. Arefeva and A.A. Slavnov, "Geometric origin of Higgs mechanism" /in Russian/, to be published

    Google Scholar 

  6. E.H. Spanier, "Algebraic Topology", Mc Graw-Hill Inc., New York 1966

    MATH  Google Scholar 

  7. V.Y. Kraines, Trans. Am. Math. Soc. 122, 357 /1966/

    Article  MathSciNet  Google Scholar 

  8. S. Ishihara, Journ. Diff. Geom. 9, 483 /1974/

    MathSciNet  Google Scholar 

  9. E.A. Ivanov and V.I. Ogievetski, TMF 25, 164 /1975/

    Google Scholar 

  10. M.S. Narasimhan and S. Ramanan, Am. J. Math. 83, 356 /1961/; 85, 223 /1963/

    Article  MathSciNet  Google Scholar 

  11. J. Lukierski, CERN preprint TH-2678, May 1979; improved version to be publ. in Proc. of Summer Institute, Kaiserslautern, August 1979, Springer Verlag

    Google Scholar 

  12. F. Gűrsey and H.C. Tze, Yale preprint, August 1979 to be published in Annals of Physics.

    Google Scholar 

  13. R. Arnowitt and P. Nath, Phys. Lett. 56 B, 177 /1975/

    MathSciNet  Google Scholar 

  14. C. Fronsdal, Letters Math. Phys. 1, 165 /1976/

    Article  MathSciNet  Google Scholar 

  15. J. Wess and B. Zumino, Phys. Lett. 56B, 361 /1977/

    Article  MathSciNet  Google Scholar 

  16. V.I. Ogievetski and E. Sokhatchev, Dubna preprints, 1979

    Google Scholar 

  17. P.G.O. Freund and I. Kaplansky, J. Math. Phys. 17, 228 /1976/

    Article  MathSciNet  Google Scholar 

  18. V. Rittenberg, in "Group — Theoretic Methods in Physics", Proc. of V Int. Symposium, Tűbingen, July 1977, publ.Springer Verlag

    Google Scholar 

  19. J. Lukierski, "Quaternionic superspaces and supersymmetric extensions of quaternionic groups", to be publ. in Proc. of Intern. Seminar of Group-Theoretical Methods, Zvenigorod /USSR/, November 1979

    Google Scholar 

  20. S. Ferrara, J. Wess and B. Zumino, Phys. Lett. B51, 239 /1974/

    Article  Google Scholar 

  21. A. Salam and J. Strathdee, Phys. Rev. D11, 1521 /1975/

    MathSciNet  Google Scholar 

  22. J. Lukierski, to be published as a lecture at Karpacz Winter School, February 1980

    Google Scholar 

  23. J. Lukierski and B. Milewski, to be published

    Google Scholar 

  24. S. Ferrara and B. Zumino, Nucl.Phys. B79, 413 /1974/

    Google Scholar 

  25. A. Salam and J. Strathdee, Phys. Lett. B51, 353 /1974/

    Article  MathSciNet  Google Scholar 

  26. D.W. Alekseevski, Funkc. Anal. i ego Prim., 2, 11 /1968/ /in Russian/

    Google Scholar 

  27. A. Gray, Michigan Math. J. 16, 125 /1969/

    Article  MathSciNet  Google Scholar 

  28. I.A. Wolf, J. Math. Mech. 14, 1033 /1965/

    MathSciNet  Google Scholar 

  29. D.W. Alekseevski, Izv. AN USSR, Ser. Mat. 39, 315 /1975/ /in Russian/

    Google Scholar 

  30. M.F. Atiyah, R. Bott and A. Shapiro, Topology, 3, /suppl.I/, 3 /1964/

    Article  MathSciNet  Google Scholar 

  31. Y.C. Wong, Proc. Acad. Sci. USA 57, 589 /1967/

    Article  Google Scholar 

  32. L. Michel and L.A. Radicati in Coral Gable Conf., 1968

    Google Scholar 

  33. H. Eichenherr, Nucl. Phys. B146, 215 /1968/

    Google Scholar 

  34. A.M. Perelomov, Comm.Math.Phys. 63, 237 /1978/

    Article  MathSciNet  Google Scholar 

  35. V. de Alfaro, S. Fubini and G. Furlan, Nuovo Cim. 50A, 523 /1979/

    Article  Google Scholar 

  36. W.E. Zacharov and A.W. Michailov, JETP 74, 1953 /1978/

    Google Scholar 

  37. A.T. Ogielski, Phys. Rev. D, in press

    Google Scholar 

  38. T.L.R. Skyrme, Proc. Roy. Soc. A260, 127 /1961/

    Article  MathSciNet  Google Scholar 

  39. N.K. Pak and H.C. Tze, Ann. of Phys. 117, 164 /1979/

    Article  MathSciNet  Google Scholar 

  40. L.D. Faddeev, Lett. in Math. Phys. 1, 289 /1976/

    Article  MathSciNet  Google Scholar 

  41. W.N. Romanov and A.C. Schwarz, TMF, 37, 305 /1978/ /in Russian/

    Google Scholar 

  42. M.A. Semenov-Tian-Szanski and L.D. Faddeev, Westnik LGU, 13, 81 /1977/

    Google Scholar 

  43. M.F. Atiyah, N.J. Hitchin, V.G. Drinfeld and Yu.I. Manin, Phys. Lett. 65A, 185 /1978/

    Article  MathSciNet  Google Scholar 

  44. F.A. Berezin, Funkc.Analiz i ego pril. 11,n.2/1979//in Russian/

    Google Scholar 

  45. R. Gilmore, "Lie groups, Lie algebras and some of its applications", Wiley-Interscience Publ., New York 1974

    MATH  Google Scholar 

  46. F.A. Berezin and G.I. Kac, Mat. Sbornik, 82, 314 /1970/

    MathSciNet  Google Scholar 

  47. J. Tits, "Tabellen zu den einfachen Lie Gruppen und ihre Darstellungen", Lect.Notes in Math., Vol.40, Springer Verlag, Berlin, 1967

    Book  MATH  Google Scholar 

  48. F.A. Berezin, Jad.Fiz. 29, 1970 /1979/

    MathSciNet  Google Scholar 

  49. A. Rogers, Imperial College prepreint, March 1979

    Google Scholar 

  50. B. Kostant, in Proc.of the Conf.on Differential-Geom.Methods. in Math.Phys.,Bonn, July 1975, publ. in Springer 1976

    Google Scholar 

  51. F.A. Berezin, Jad.Fiz. 30, 1168 /1979/

    MathSciNet  Google Scholar 

  52. J. Lukierski, in "Supergravity" ed. P.van Nieuwenhuizen and D.Z. Freedman, North-Holland, 1979, p. 301.

    Google Scholar 

  53. J. Lukierski, ICTP preprint 78/82, J. Math. Phys., in press

    Google Scholar 

  54. J. Lukierski, Lett. Math. Phys. 3, 135 /1979/

    Article  MathSciNet  Google Scholar 

  55. J. Lukierski, "Quarks and Fermionic Geometry", Lecture at IV Hadronic Workshop, Erice, October 1978; in Proceedings, in press; see also Czech. Journ. Phys. 29, 44 /1979/

    Google Scholar 

  56. A. Trautman, Int. J. Theor. Phys. 16, 561 /1977/

    Article  Google Scholar 

  57. P. di Vecchia and S. Ferrara, Nucl. Phys. B130, 93 /1977/

    Article  Google Scholar 

  58. E. Witten, Phys. Rev. 16, 2991 /1977/

    Google Scholar 

  59. B. Zumino, CERN preprint TH-2733, August 1979

    Google Scholar 

  60. A. d'Adda, P. di Vecchia and M. Lüscher, Nucl. Phys. B152, 125 /1979/

    Article  Google Scholar 

  61. A.W. Michailov and A.M. Perelomov, JETP Letters 29, 445 /1979/

    Google Scholar 

  62. A.B. Borisov and V.I. Ogievetski, TMF 21, 329 /1974/

    Google Scholar 

  63. E. Cremmer and B. Julia, Nucl.Phys. B159, 141 /1979/

    Article  MathSciNet  Google Scholar 

  64. J.G. Taylor, Phys. Rev. Lett. 43, 824 /1979/

    Article  Google Scholar 

  65. A. Salam, unpublished

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Theoretical Physics, University of Wrocław, ul. Cybulskiego 36, Wrocław, Poland

    Jerzy Lukierski

Authors
  1. Jerzy Lukierski
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

P. L. García A. Pérez-Rendón J. M. Souriau

Rights and permissions

Reprints and permissions

Copyright information

© 1980 Springer-Verlag

About this paper

Cite this paper

Lukierski, J. (1980). Quaternionic and supersymmetric σ — models. In: García, P.L., Pérez-Rendón, A., Souriau, J.M. (eds) Differential Geometrical Methods in Mathematical Physics. Lecture Notes in Mathematics, vol 836. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089738

Download citation

  • DOI: https://doi.org/10.1007/BFb0089738

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10275-5

  • Online ISBN: 978-3-540-38405-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation