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)=S 3 →S 2 andSp(2)/Sp(1)=S 7 →S 4, 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.
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References
Belavin, A. A., Polyakov, A. M., Schwartz, A. S., and Tyupkin, Yu. S. (1975).Physics Letters,59B, 85.
Callan, C. G. Jr., Dashen, R. F., and Gross, D. J. (1976).Physics Letters,63B, 334.
Chern, S. S. (1967).Complex manifolds without potential theory. Van Nostrand, New York.
Dirac, P. A. M. (1931).Proceedings of the Royal Society of London,A133, 60.
Eguchi, T. and Freund, P. G. O. (1976).Physical Review Letters,37, 1251.
Ezawa, Z. F. and Tze, H. C. (1976).Journal of Mathematical Physics,17, 2228; and the papers quoted there.
Finkelstein, D., Jauch, J. M., Schiminovich, S., and Speiser, D. (1963).Journal of Mathematical Physics,4, 788.
Goldhaber, A. S. (1976).Physical Review Letters,36, 1122.
Goldhaber, A. S. and Smith, J. (1975).Reports on Progress in Physics,38, 731 (1975).
Greenberg, M. J. (1967).Lectures on Algebraic Topology, W. A. Benjamin, Reading, Massachusetts.
Hofft, G.'t (1976a).Physical Review Letters,37, 8; (1976b).Physical Review,D14, 3432.
Hopf, H. (1931).Mathematische Annalen,104, 637.
Husemoller, D. (1966).Fibre Bundles. McGraw-Hill Book Co., New York.
Jackiw, R. and Rebbi, C. (1976a).Physical Review Letters 37, 172.
Jackiw, R. and Rebbi, C. (1976b).Physical Review D,14, 517.
Lubkin, E. (1963).Annals of Physics,23, 233.
Morrow, J. and Kodaira, K. (1971).Complex Manifolds. Holt, Rinehart and Winston, Inc., New York.
Nambu, Y. (1974).Physical Review D,10, 4262.
Parker, L. (1975).Physical Review Letters,34, 412.
Steenrod, N. (1951).The Topology of Fibre Bundles. Princeton University Press, Princeton, New Jersey.
Trautman, A. (1970).Reports on Mathematical Physics (Toruń),1, 29.
Weil, A. (1958).Introduction à l'étude des variétés kähleriennes, Hermann, Paris.
Wu, T. T. and Yang, C. N. (1975).Physical Review D,12, 3845.
Wu, T. T. and Yang, C. N. (1976).Physical Review D,14, 437 (1976).
Yang, C. N. (1977).Physical Review D, (to be published).
Yang, C. N. and Mills, R. L. (1954).Physical Review,96, 191
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On leave from the Institute of Theoretical Physics, Warsaw University, Hoza 69, Warsaw, Poland.
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Trautman, A. Solutions of the Maxwell and Yang-Mills equations associated with hopf fibrings. Int J Theor Phys 16, 561–565 (1977). https://doi.org/10.1007/BF01811088
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DOI: https://doi.org/10.1007/BF01811088