International Journal of Theoretical Physics

, Volume 16, Issue 8, pp 561–565

Solutions of the Maxwell and Yang-Mills equations associated with hopf fibrings

  • Andrzej Trautman
Article

Abstract

It is shown that the magnetic pole of lowest strength and the pseudoparticle solution of the Yang-Mills equations correspond to natural connections defined on the principal bundlesU(2)/U(1)=S3S2 andSp(2)/Sp(1)=S7S4, respectively. This observation leads to a general methods of constructing new, topologically nontrivial solutions of the Maxwell and Yang-Mills equations. Among them is an “electromagnetic instanton” defined over the two-dimensional complex projective space endowed with the Fubini-Study metric.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Belavin, A. A., Polyakov, A. M., Schwartz, A. S., and Tyupkin, Yu. S. (1975).Physics Letters,59B, 85.ADSMathSciNetGoogle Scholar
  2. Callan, C. G. Jr., Dashen, R. F., and Gross, D. J. (1976).Physics Letters,63B, 334.ADSGoogle Scholar
  3. Chern, S. S. (1967).Complex manifolds without potential theory. Van Nostrand, New York.MATHGoogle Scholar
  4. Dirac, P. A. M. (1931).Proceedings of the Royal Society of London,A133, 60.CrossRefADSGoogle Scholar
  5. Eguchi, T. and Freund, P. G. O. (1976).Physical Review Letters,37, 1251.CrossRefADSMathSciNetGoogle Scholar
  6. Ezawa, Z. F. and Tze, H. C. (1976).Journal of Mathematical Physics,17, 2228; and the papers quoted there.CrossRefADSMathSciNetGoogle Scholar
  7. Finkelstein, D., Jauch, J. M., Schiminovich, S., and Speiser, D. (1963).Journal of Mathematical Physics,4, 788.MATHCrossRefADSMathSciNetGoogle Scholar
  8. Goldhaber, A. S. (1976).Physical Review Letters,36, 1122.CrossRefADSGoogle Scholar
  9. Goldhaber, A. S. and Smith, J. (1975).Reports on Progress in Physics,38, 731 (1975).CrossRefADSGoogle Scholar
  10. Greenberg, M. J. (1967).Lectures on Algebraic Topology, W. A. Benjamin, Reading, Massachusetts.MATHGoogle Scholar
  11. Hofft, G.'t (1976a).Physical Review Letters,37, 8; (1976b).Physical Review,D14, 3432.CrossRefADSGoogle Scholar
  12. Hopf, H. (1931).Mathematische Annalen,104, 637.CrossRefMathSciNetGoogle Scholar
  13. Husemoller, D. (1966).Fibre Bundles. McGraw-Hill Book Co., New York.MATHGoogle Scholar
  14. Jackiw, R. and Rebbi, C. (1976a).Physical Review Letters 37, 172.CrossRefADSGoogle Scholar
  15. Jackiw, R. and Rebbi, C. (1976b).Physical Review D,14, 517.CrossRefADSMathSciNetGoogle Scholar
  16. Lubkin, E. (1963).Annals of Physics,23, 233.CrossRefADSMathSciNetGoogle Scholar
  17. Morrow, J. and Kodaira, K. (1971).Complex Manifolds. Holt, Rinehart and Winston, Inc., New York.MATHGoogle Scholar
  18. Nambu, Y. (1974).Physical Review D,10, 4262.CrossRefADSGoogle Scholar
  19. Parker, L. (1975).Physical Review Letters,34, 412.CrossRefADSGoogle Scholar
  20. Steenrod, N. (1951).The Topology of Fibre Bundles. Princeton University Press, Princeton, New Jersey.MATHGoogle Scholar
  21. Trautman, A. (1970).Reports on Mathematical Physics (Toruń),1, 29.MATHCrossRefMathSciNetGoogle Scholar
  22. Weil, A. (1958).Introduction à l'étude des variétés kähleriennes, Hermann, Paris.MATHGoogle Scholar
  23. Wu, T. T. and Yang, C. N. (1975).Physical Review D,12, 3845.CrossRefADSMathSciNetGoogle Scholar
  24. Wu, T. T. and Yang, C. N. (1976).Physical Review D,14, 437 (1976).CrossRefADSMathSciNetGoogle Scholar
  25. Yang, C. N. (1977).Physical Review D, (to be published).Google Scholar
  26. Yang, C. N. and Mills, R. L. (1954).Physical Review,96, 191CrossRefADSMathSciNetGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • Andrzej Trautman
    • 1
  1. 1.Institute for Theoretical PhysicsState University of New York at Stony BrookStony Brook

Personalised recommendations