eprintid: 10196914
rev_number: 10
eprint_status: archive
userid: 699
dir: disk0/10/19/69/14
datestamp: 2024-10-11 06:29:12
lastmod: 2024-10-11 06:29:12
status_changed: 2024-10-11 06:29:12
type: thesis
metadata_visibility: show
sword_depositor: 699
creators_name: Mendizabal, Jaime
title: On Monopoles with Arbitrary Symmetry Breaking and their Moduli Spaces
ispublished: unpub
divisions: UCL
divisions: B04
divisions: C06
note: Copyright © The Author 2024.  Original content in this thesis is licensed under the terms of the Creative Commons Attribution 4.0 International (CC BY 4.0) Licence (https://creativecommons.org/licenses/by/4.0/).  Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms.  Access may initially be restricted at the author’s request.
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.
date: 2024-09-28
date_type: published
oa_status: green
full_text_type: other
thesis_class: doctoral_open
thesis_award: Ph.D
language: eng
primo: open
primo_central: open_green
verified: verified_manual
elements_id: 2312027
lyricists_name: Mendizabal Roche, Jaime
lyricists_id: JMEND27
actors_name: Mendizabal Roche, Jaime
actors_name: Zahnhausen-Stuber, Petra
actors_id: JMEND27
actors_id: PMZAH20
actors_role: owner
actors_role: impersonator
full_text_status: public
pagerange: 1-148
pages: 148
institution: UCL (University College London)
department: Mathematics
thesis_type: Doctoral
citation:        Mendizabal, Jaime;      (2024)    On Monopoles with Arbitrary Symmetry Breaking and their Moduli Spaces.                   Doctoral thesis  (Ph.D), UCL (University College London).     Green open access   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/10196914/1/Mendizabal_thesis.pdf