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Mat. Sb., 2010, Volume 201, Number 6, Pages 19–74 (Mi msb7560)  

This article is cited in 5 scientific papers (total in 5 papers)

$\operatorname{SU}(2)$-monopoles, curves with symmetries and Ramanujan's heritage

H. W. Bradena, V. Z. Enolskib

a University of Edinburgh, UK
b Institute of Magnetism, National Academy of Sciences of Ukraine

Abstract: We develop the Ercolani-Sinha construction of SU(2) monopoles for a five-parameter family of centred charge 3 monopoles. In particular we show how to solve the transcendental constraints arising on the spectral curve. For a class of symmetric curves the transcendental constraints become a number-theoretic problem and a recently proven identity of Ramanujan provides a solution.
Bibliography: 36 titles.

Keywords: non-Abelian monopole, Ramanujan's hypergeometric identities, algebraic curves with automorphisms.

DOI: https://doi.org/10.4213/sm7560

Full text: PDF file (987 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2010, 201:6, 801–853

Bibliographic databases:

Document Type: Article
UDC: 517.958:530.145.83+515.178.2+517.58
MSC: Primary 81T13, 14H70, 14H45; Secondary 14K25, 33Cxx
Received: 19.03.2009

Citation: H. W. Braden, V. Z. Enolski, “$\operatorname{SU}(2)$-monopoles, curves with symmetries and Ramanujan's heritage”, Mat. Sb., 201:6 (2010), 19–74; Sb. Math., 201:6 (2010), 801–853

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm7560
  • http://mi.mathnet.ru/eng/msb/v201/i6/p19

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Braden H.W., Northover T.P., “Klein's curve”, J. Phys. A, 43:43 (2010), 434009, 17 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    2. Braden H.W., Enolski V.Z., “On the existence of non-abelian monopoles: the algebro-geometric approach”, XXIX Workshop on Geometric Methods in Physics, AIP Conf. Proc., 1307, Amer. Inst. Phys., Melville, NY, 2010, 53–67  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    3. H. W. Braden, V. Z. Ènol'skii, “Some remarks on the Ercolani–Sinha construction of monopoles”, Theoret. and Math. Phys., 165:3 (2010), 1567–1597  mathnet  crossref  crossref  isi
    4. Braden H.W., D'Avanzo A., Enolski V.Z., “On charge-3 cyclic monopoles”, Nonlinearity, 24:3 (2011), 643–675  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    5. Braden H.W., “Cyclic monopoles, affine Toda and spectral curves”, Comm. Math. Phys., 308:2 (2011), 303–323  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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