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Some comments on the non-self-dual Nahm equations

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Abstract

Some empirical results on the cubic algebra\(2a_i = \sum\limits_j {[a_{j,} [a_{j,} a_i ]]} \) are presented. The algebra is satisfied at the residue of any pole in a solution to Nahm's non-self-dual equations.

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References

  1. Baseyan, G.Z., Martinyan, S.G., Savviddy, G.K.: Non-linear plane waves in the massless Yang-Mills theory. Pis'ma Zh. Gksp. Teor. Prakt. Fiz. Kul.29, 641 (1979)

    Google Scholar 

  2. Nikolaevskii, E.S., Schur, L.N.: Non-integrability of the classical Yang-Mills fields. JETP Letts.36, 218 (1982)

    Google Scholar 

  3. Savviddy, G.K.: The Yang-Mills classical mechanics as a KolmogarovK-system. Phys. Letts.130 B, 303 (1983)

    Google Scholar 

  4. Chang, S.J.: Classical Yang-Mills solutions and iterative maps. Phys. Rev. D29, 259 (1984)

    Google Scholar 

  5. Atiyah, M.F., Hitchin, N.J., Drinfeld, V.G., Manin, Yu.I.: Construction of instantons. Phys. Letts. B65 A, 185 (1978)

    Google Scholar 

  6. Drinfeld, V.G., Manin, Yu.I.: A description of instantons. Commun. Math. Phys.63, 177 (1978)

    Google Scholar 

  7. Nahm, W.: Multimonopoles in the ADHM construction. In: Proceedings of the symposium on particle physics. Horvath, Z., et al. (eds.), Visegrad 1981

  8. Nahm, W.: Construction of all self-dual monopoles by the ADHM method. In: Monopoles and quantum field theory. Craigie, N., et al. (eds.), Singapore: World Scientific 1982

    Google Scholar 

  9. Hitchin, N.J.: On the construction of monopoles. Commun. Math. Phys.89, 145 (1983)

    Google Scholar 

  10. Bogoml'nyi, E.B.: The stability of classical solutions. Sov. J. Nucl. Phys.24, 449 (1976)

    Google Scholar 

  11. Prasad, M.K., Sommerfield, C.M.: Exact classical solution for the 't Hooft monopole and Julia-Zee dyon. Phys. Rev. Lett.35, 760 (1975)

    Google Scholar 

  12. Corrigan, E.: A brief introduction to the monopole. Talk given at 11th winter school on abstract analysis. Zelezna Ruda, Czechoslovakia, Jan. 1983

  13. Corrigan, E., Goddard, P.: Construction of instanton and monopole solutions and reciprocity. Ann. Phys. (N.Y.)154, 352 (1984)

    Google Scholar 

  14. Nahm, W.: Self dual monopoles and calorons. Talk given at XII colloquium on group theoretical methods in physics. Trieste, September 1983

  15. Taubes, C.: The existence of a non-minimal solution to the SU(2) Yang-Mills-Higgs equations on ℝ3. Commun. Math. Phys.86, 257 (1982)

    Google Scholar 

  16. Erdelyi, A., et al.: Higher transcendental functions, Vol. II. New York: McGraw-Hill 1953

    Google Scholar 

  17. Wybourne, B.G.: Classical groups for physicists. New York: Wiley 1974

    Google Scholar 

  18. Cvitanovic, P., Myrheim, J.: Complex universality. Nordita preprint 84/5

  19. Manton, N.S., Nauenberg, M.: Universal scaling behaviour for iterated maps in the complex plane. Commun. Math. Phys.89, 555 (1983)

    Google Scholar 

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Communicated by A. Jaffe

Sir Derman Christopherson Foundation Fellow

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Corrigan, E., Wainwright, P.R. & Wilson, S.M.J. Some comments on the non-self-dual Nahm equations. Commun.Math. Phys. 98, 259–272 (1985). https://doi.org/10.1007/BF01220513

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