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Some remarks on the Ercolani—Sinha construction of monopoles

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Abstract

We develop the Ercolani—Sinha construction of SU(2) monopoles, which provides a gauge transform of the Nahm data.

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References

  1. N. Manton and P. Sutcliffe, Topological Solitons, Cambridge Univ. Press, Cambridge (2004).

    Book  MATH  Google Scholar 

  2. N. J. Hitchin, Comm. Math. Phys., 83, 579–602 (1982).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  3. N. J. Hitchin, Comm. Math. Phys., 89, 145–190 (1983).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  4. W. Nahm, “The construction of all self-dual multimonopoles by the ADHMmethod,” in: Monopoles in Quantum Field Theory (N. S. Craigie, P. Goddard, and W. Nahm, eds.), World Scientific, Singapore (1982), pp. 87–94.

    Google Scholar 

  5. N. Ercolani and A. Sinha, Comm. Math. Phys., 125, 385–416 (1989).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  6. B. A. Dubrovin, Funct. Anal. Appl., 11, No. 4, 265–277 (1977).

    Article  MathSciNet  Google Scholar 

  7. H. W. Braden and V. Z. Enolski, “Remarks on the complex geometry of the 3-monopole,” arXiv:mathph/0601040v1 (2006).

  8. H. W. Braden and V. Z. Énol’skii, Sb. Math., 201, 801–853 (2010).

    Article  MATH  MathSciNet  Google Scholar 

  9. H. W. Braden and V. Z. Enolski, Comm. Math. Phys., 299, 255–282 (2010); arXiv:0908.3449v1 [math-ph] (2009).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  10. H. W. Braden and V. Z. Enolski, Glasgow Math. J., 51, No. A, 25–41 (2009); arXiv:0806.1807v1 [math-ph] (2008).

    Article  MathSciNet  Google Scholar 

  11. J. Hurtubise, Comm. Math. Phys., 92, 195–202 (1983).

    Article  MathSciNet  ADS  Google Scholar 

  12. E. Corrigan and P. Goddard, Comm. Math. Phys., 80, 575–587 (1981).

    Article  MathSciNet  ADS  Google Scholar 

  13. J. D. Fay, Theta Functions on Riemann Surfaces (Lect. Notes Math., Vol. 352), Springer, Berlin (1973).

    Google Scholar 

  14. A. Clebsch and P. Gordan, Theorie der Abelschen Funktionen, Teubner, Leipzig (1866).

    Google Scholar 

  15. Yu. Fedorov, Acta Appl. Math., 55, 251–301 (1999).

    Article  MATH  MathSciNet  Google Scholar 

  16. H. W. Braden and Yu. N. Fedorov, J. Geom. Phys., 58, 1346–1354 (2008); arXiv:math-ph/0701045v1 (2007).

    Article  MathSciNet  ADS  Google Scholar 

  17. H. F. Baker, Abel’s Theorem and the Allied Theory of Theta Functions, Cambridge Univ. Press, Cambridge (1897, reprinted 1995).

    MATH  Google Scholar 

  18. J.-Ichi Igusa, Theta Functions (Grund. Math. Wiss., Vol. 194), Springer, Berlin (1972).

    Google Scholar 

  19. H. M. Farkas and I. Kra, Riemann Surfaces (Grad. Texts in Math., Vol. 71), Springer, New York (1980).

    Google Scholar 

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Authors and Affiliations

  1. School of Mathematics, Edinburgh University, Edinburgh, UK

    H. W. Braden

  2. Hanse-Wissenschaftskolleg (Institute for Advanced Study), Delmenhorst, Germany

    V. Z. Enolski

  3. Institute of Magnetism, National Academy of Sciences of Ukraine, Kiev, Ukraine

    V. Z. Enolski

Authors
  1. H. W. Braden
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  2. V. Z. Enolski
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Additional information

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 165, No. 3, pp. 389–425, December, 2010.

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Braden, H.W., Enolski, V.Z. Some remarks on the Ercolani—Sinha construction of monopoles. Theor Math Phys 165, 1567–1597 (2010). https://doi.org/10.1007/s11232-010-0131-2

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  • DOI: https://doi.org/10.1007/s11232-010-0131-2

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