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Peter Horváthy

2011-01-14
14:00:00 - 15:30:00

R102 , Astronomy and Mathematics Building

With respect to ``Brandt-Neri-Coleman type'' variations (a) the stability problem of monopoles reduces to that of a pure gauge theory on the two-sphere, studied before by Atiyah and Bott in more generality, (b) each topological sector admits one, and only one, stable monopole charge, and (c) each unstable monopole admits $\displaystyle{2\sum_{q<0} \left(2|q|-1\right)}$ negative modes, where the sum goes over all negative eigenvalues $q$ of the non-Abelian charge $Q$ of Goddard-Nuyts and Olive. An explicit construction for (i) the unique stable charge (ii) the negative modes and (iii) the spectrum of the Hessian, on the $2$-sphere, is then given. The relation to loops in the residual group is explained. The negative modes are tangent to suitable energy-reducing two-spheres.

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