Mendizabal, Jaime; (2024) On Monopoles with Arbitrary Symmetry Breaking and their Moduli Spaces. Doctoral thesis (Ph.D), UCL (University College London).

Preview

Text Mendizabal_thesis.pdf - Other Download (1MB) | Preview

Abstract

The subject of this thesis is monopoles { solutions to the Bogomolny equations { on the Euclidean 3-space R3, with arbitrary gauge group, mass and charge, and hence symmetry breaking. We start by providing an overview of monopoles themselves and discussing their asymptotics in relation to mass and charge. These are used to de ne a framing, using an asymptotic model for each such choice. With this we set up an analytic framework appropriate for the construction of moduli spaces of framed monopoles. The construction is then carried out as a quotient of in nitedimensional spaces, which requires a careful analysis of the di erential operators involved and their Fredholmness and other mapping properties. More speci cally, a combination of the b and scattering calculuses is used to de ne appropriate Sobolev spaces and analyse the partial di erential equations. The resulting framed moduli spaces are constructed as smooth manifolds and we see that they also carry hyper- Kähler metrics, obtained through a hyper-Kähler quotient construction. Lastly we consider how our results t into some of the pre-existing knowledge in this area. In particular, we discuss the relationship between the mass and the charge and the symmetry breaking, and expand upon these concepts in the cases of special unitary and orthogonal groups.

Download activity - last month

Export as CSVXMLJSON

Download activity - last 12 months

Export as CSVJSONXML

Downloads by country - last 12 months

Export as JSONXMLCSV

Archive Staff Only

View Item