Advertisement

Multimonopoles

  • E. Corrigan
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 151)

Abstract

It is difficult to see how to proceed further along the lines described above because the explicit construction of solutions involves the solution of polynomial equations of arbitrary degree. Moreover the constraints occur in terms of transcendental functions defined by contour integrals of which eqn. (5.16) is the simplest example.

On the other hand,optimistically, it may be possible to recreate the whole structure for bigger gauge groups and see the generalisation of the work described, for example, in ref. (5). It may also be possible to understand the relationship between the several ways of looking at monopoles — via ADHM(17), Bäcklund transformations (8,30) and the work described in these lectures. There is clearly much to be done and only time will tell whether this particular brand of four-dimensional soliton is a true hint of integrability in four dimensions.

Keywords

Gauge Theory Vector Bundle Gauge Field Magnetic Charge Toda Lattice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A.C.Scott, F.Y.F.Chiu and D.W.McLaughlin, Proceedings of the IEEE Vol. 61, No. 10 (1973) 1443.Google Scholar
  2. 2.
    G. 't Hooft, Nucl. Phys. B 79 (1974 276.CrossRefGoogle Scholar
  3. 2a.
    A.M.Polyakov, JETP Lett. 20 (1974) 194Google Scholar
  4. 3.
    For a review see P. Goddard and D. Olive, Reports on Progress in Physics 41 (1978) 1357.Google Scholar
  5. 4.
    E.B.Bogomolny, Sov. J. Nucl. Phys. 24 (1976) 449.Google Scholar
  6. 4a.
    S. Coleman, S. Parke, A. Neveu and C.M.Sommerfield, Phys. Rev. D15 (1977) 544.Google Scholar
  7. 5.
    For a review of this see D. Olive, ‘Classical solutions in gauge theories-spherically symmetric monopoles-Lax pairs and Toda Lattices', lectures given at the International Summer Institute on Theoretical Physics, Bad Honnef. September 1980.Google Scholar
  8. 6.
    N. Manton, Nucl. Phys. B126 (1977) 525.Google Scholar
  9. 6a.
    L. O'Raifeartaigh, S. Y.Park, K.C.Wali, Phys. Rev. 20D (1979) 1941.Google Scholar
  10. 7.
    C. Taubes, ‘Existence of multi-monopole solutions’ to appear in Comm. Math. Phys.Google Scholar
  11. 7a.
    A. Jaffe and C. Taubes, Vortices and Monopoles (Birkhauser, Boston 1980).Google Scholar
  12. 8.
    P. Forgacs, Z. Horvath and L. Palla, Phys. Lett. 99B (1981) 232.Google Scholar
  13. 9.
    R.S.Ward, ‘A Yang Mills-Higgs monopole of charge 2’ to appear in Comm. Math. Phys.Google Scholar
  14. 10.
    F. Ernst, Phys. Rev. 167 (1968) 1175.CrossRefGoogle Scholar
  15. 11.
    B.K.Harrison, Phys. Rev. Lett. 41 (1978) 1197.Google Scholar
  16. 11a.
    G. Neugebauer, J. Phys. A12 (1979) L67.Google Scholar
  17. 12.
    M.K.Prasad and C.M.Sommerfield, Phys. Rev. Lett. 35 (1975) 760.Google Scholar
  18. 13.
    E.Corrigan, D.B.Fairlie, J. Nuyts and D. Olive, Nucl. Phys. B106 (1976) 475.Google Scholar
  19. 14.
    E.B.Bogomolny, Sov. J. Nucl. Phys. 24 (1976) 449.Google Scholar
  20. 15.
    For reviews see for example D. Olive, Rivista del Nuovo Cimento 2 (1979) 1.Google Scholar
  21. 15a.
    E. Corrigan, Phys. Reps. 49C (1979) 95.Google Scholar
  22. 15b.
    M.F.Atiyah, Geometry of Yang Mills Fields, Lezione Fermioni, Pisa 1979.Google Scholar
  23. 15c.
    E. Corrigan and P. Goddard, Lecture notes in Physics 129, Geometrical and Topological Methods in Gauge Theories, Eds. J.P.Harnad and S. Shnider (Springer Verlag 1980).Google Scholar
  24. 16.
    M.F.Atiyah, N.J.Hitchin, V.G.Drinfeld and Yu I. Manin, Phys. Letts. 65A (1978) 185.Google Scholar
  25. 17.
    W. Nahm, Phys. Letts. 90B (1980) 413, 93B (1980) 42.Google Scholar
  26. 18.
    R.S.Ward, Phys. Letts. 61A (1977) 81.Google Scholar
  27. 19.
    M.F.Atiyah and R.S.Ward, Comm. Math. Phys. 55 (1977) 117.Google Scholar
  28. 20.
    F. Wilczek, Quark Confinement and Field Theory, eds. D. Stump and D. Weingarten (John Wiley and Sons, New York (1977)).Google Scholar
  29. 20a.
    E. Corrigan and D.B.Fairlie, Phys. Letts. 67B (1977) 69.Google Scholar
  30. 20b.
    R.Jackiw, C. Nohl and C. Rebbi, Phys. Rev. D15 (1977) 1642.Google Scholar
  31. 21.
    N. Manton, Nucl. Phys. B135 (1978) 319.Google Scholar
  32. 22.
    M.K.Prasad and P. Rossi, MIT Preprint CTP 903 (1980).Google Scholar
  33. 23.
    E. Weinberg, Phys. Rev. D20 (1979) 936.Google Scholar
  34. 24.
    C.N.Yang, Phys. Rev. Letts. 38 (1977) 1377.Google Scholar
  35. 25.
    E. Corrigan, D.B.Fairlie, P. Goddard and R. Yates, Comm. Math. Phys. 58 (1978) 2528.Google Scholar
  36. 26.
    A useful review of this section is in M.K.Prasad, Physica ID (1980) 167.Google Scholar
  37. 27.
    M.A.Lohe, Nucl. Phys. B142 (1978) 236.Google Scholar
  38. 27a.
    D.J.Bruce, Nucl. Phys. B142 (1978) 253.Google Scholar
  39. 28.
    M.K.Prasad, ‘Exact Yang-Mills-Higgs Monopole solutions of arbitrary topological charge', Comm. Math. Phys. to be published.Google Scholar
  40. 29.
    R.S.Ward, ‘Two Yang-Mills-Higgs monopoles close together’ Dublin preprint, March 1981.Google Scholar
  41. 30.
    P. Forgacs, Z. Horvath and L. Palls, ‘Non-linear superposition of monopoles’ March 1981.Google Scholar
  42. 31.
    E. Corrigan and P. Goddard, ‘An n monopole solution with 4n-1 degrees of freedom’ DAMTP 81/9 March 1981.Google Scholar
  43. 32.
    L. O'Raifeartaigh and S. Rouhani, Schladming lectures (1981), Dublin preprint DIAS-STP-81-03.Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • E. Corrigan
    • 1
  1. 1.Department of MathematicsUniversity of DurhamUK

Personalised recommendations