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Communications in Mathematical Physics

, Volume 330, Issue 2, pp 539–580 | Cite as

Magnetic Bag Like Solutions to the SU(2) Monopole Equations on \({{\mathbb R}^{3}}\)

  • Clifford Henry TaubesEmail author
Article

Abstract

Solutions to the SU(2) monopole equations in the Bogolmony limit are constructed that look very much like Bolognesis conjectured magnetic bag solutions. Three theorems are also stated and proved that give bounds in terms of the topological charge for the radii of balls where the solutions Higgs field has very small norm.

Keywords

Banach Space Topological Charge Product Bundle Dirac Monopole Associate Vector Bundle 
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.

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References

  1. Bol.
    Bolognesi S.: Multi-monopoles and magnetic bags. Nucl. Phys. B 752(1-2), 93–123 (2006)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  2. EG.
    Evslin, J., Gudnason, S.B.: High Q BPS monopole bags are urchins (2011)Google Scholar
  3. H.
    Harland D.: The large N limit of the Nahm transform. Commun. Math. Phys. 311(3), 689–712 (2012)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  4. HPS.
    Harland D., Palmer S., Saemann C.: Magnetic domains. JHEP 1210, 167 (2012)ADSCrossRefGoogle Scholar
  5. JT.
    Jaffe A., Taubes C.: Vortices and monopoles. In: Progress in Physics. Mass Structure of Static Gauge Theories, Vol. 2, Boston, Birkhäuser, 1980Google Scholar
  6. LW.
    Lee K.-M., Weinberg E.J.: Bps magnetic monopole bags. Phys. Rev. D 79(2), 025013–025018 (2009)ADSCrossRefMathSciNetGoogle Scholar
  7. M.
    Manton N.S.: Monopole planets and galaxies. Phys.Rev. D 85, 045022 (2012)ADSCrossRefGoogle Scholar
  8. PS.
    Prasad M.K., Sommerfield C.M.: Exact classical solution for the ’t hooft monopole and the julia-zee dyon. Phys. Rev. Lett. 35, 760–762 (1975)ADSCrossRefGoogle Scholar
  9. RSZ.
    Rakhmanov, E.A., Saff, E.B., Zhou, Y.M.: Electrons on the sphere. In: Computational Methods and Function Theory 1994 (Penang), Ser. Approx. Decompos., Vol. 5, River Edge, World Sci. Publ., 1995, pp. 293–309Google Scholar
  10. R.
    Royden H. L.: Real Analysis, 3rd edn. Macmillan Publishing Company, New York (1988)zbMATHGoogle Scholar
  11. KS.
    Saff E.B., Kuijlaars A.B.J.: Distributing many points on a sphere. Math. Intell. 19(1), 5–11 (1997)CrossRefzbMATHMathSciNetGoogle Scholar
  12. S1.
    Singleton D.: Exact Schwarzschild-like solution for Yang–Mills theories. Phys. Rev. D (3) 51(10), 5911–5914 (1995)ADSCrossRefMathSciNetGoogle Scholar
  13. S2.
    Singleton D.: Yang–Mills analogues of general relativistic solutions. Theor. Math. Fiz. 117(2), 308–324 (1998)CrossRefMathSciNetGoogle Scholar
  14. T.
    Taubes, C.H.: A gauge invariant index theorem for asymptotically flat manifolds. In: Asymptotic Behavior of Mass and Spacetime Geometry (Corvallis, Ore., 1983), Lecture Notes in Physics, Vol. 202, Berlin, Springer, 1984, pp. 85–94Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of MathematicsHarvard UniversityCambridgeUSA

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