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.
Similar content being viewed by others
References
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)
Nikolaevskii, E.S., Schur, L.N.: Non-integrability of the classical Yang-Mills fields. JETP Letts.36, 218 (1982)
Savviddy, G.K.: The Yang-Mills classical mechanics as a KolmogarovK-system. Phys. Letts.130 B, 303 (1983)
Chang, S.J.: Classical Yang-Mills solutions and iterative maps. Phys. Rev. D29, 259 (1984)
Atiyah, M.F., Hitchin, N.J., Drinfeld, V.G., Manin, Yu.I.: Construction of instantons. Phys. Letts. B65 A, 185 (1978)
Drinfeld, V.G., Manin, Yu.I.: A description of instantons. Commun. Math. Phys.63, 177 (1978)
Nahm, W.: Multimonopoles in the ADHM construction. In: Proceedings of the symposium on particle physics. Horvath, Z., et al. (eds.), Visegrad 1981
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
Hitchin, N.J.: On the construction of monopoles. Commun. Math. Phys.89, 145 (1983)
Bogoml'nyi, E.B.: The stability of classical solutions. Sov. J. Nucl. Phys.24, 449 (1976)
Prasad, M.K., Sommerfield, C.M.: Exact classical solution for the 't Hooft monopole and Julia-Zee dyon. Phys. Rev. Lett.35, 760 (1975)
Corrigan, E.: A brief introduction to the monopole. Talk given at 11th winter school on abstract analysis. Zelezna Ruda, Czechoslovakia, Jan. 1983
Corrigan, E., Goddard, P.: Construction of instanton and monopole solutions and reciprocity. Ann. Phys. (N.Y.)154, 352 (1984)
Nahm, W.: Self dual monopoles and calorons. Talk given at XII colloquium on group theoretical methods in physics. Trieste, September 1983
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)
Erdelyi, A., et al.: Higher transcendental functions, Vol. II. New York: McGraw-Hill 1953
Wybourne, B.G.: Classical groups for physicists. New York: Wiley 1974
Cvitanovic, P., Myrheim, J.: Complex universality. Nordita preprint 84/5
Manton, N.S., Nauenberg, M.: Universal scaling behaviour for iterated maps in the complex plane. Commun. Math. Phys.89, 555 (1983)
Author information
Authors and Affiliations
Additional information
Communicated by A. Jaffe
Sir Derman Christopherson Foundation Fellow
Rights and permissions
About this article
Cite this article
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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01220513