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The charge density of a monopole and its asymptotic tail

Thursday 30th July 2015 - 14:30 to 15:30
INI Seminar Room 1
Co-author: Daniel Nogradi

Magnetic monopoles are finite-energy solutions of the Yang-Mills-Higgs equations in non-abelian gauge theory. From afar, they resemble sources of magnetic charge in Maxwell electromagnetism (hence the name). It is a long-standing problem to identify a smooth magnetic charge density which induces the asymptotic magnetic field of a monopole. In this talk I will present a novel solution to this problem. I define a charge density by summing the squared norms of an L^2-orthonormal basis for the kernel of a Dirac operator associated with the monopole -- this is the analog for monopoles of the Bergman kernel in Kaehler geometry. I will show that the expansion of its induced magnetic field agrees with the asymptotic field of the monopole, to all orders in 1/r. I will also discuss the explicit evaluation of this asymptotic field.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons