Higher Gauge Theory
dc.rights.license | CC-BY-NC-ND | |
dc.contributor.advisor | Cavalcanti, G.R. | |
dc.contributor.advisor | Alekseev, A. | |
dc.contributor.author | Voorhaar, W.H. | |
dc.date.accessioned | 2018-02-26T18:01:03Z | |
dc.date.available | 2018-02-26T18:01:03Z | |
dc.date.issued | 2018 | |
dc.identifier.uri | https://studenttheses.uu.nl/handle/20.500.12932/28688 | |
dc.description.abstract | We generalize several aspects of gauge theory to 2-gauge theory. We consider 2-transport on principal 2-bundles with strict 2-group fiber by categorifying a usual definition of principal bundles, following work by Schreiber and Waldorf. We show that locally 2-transport induces a 2-functor from the 2-groupoid of bigons up to thin homotopy to the 2-group. By generalizing the non-Abelian Stokes' Theorem to the 2-group setting, we are able to prove a direct generalization of the Ambrose-Singer Theorem for 2-bundles. Finally we further develop the theory of surface holonomy. In particular we elucidate how such a theory depends on the choice of marking of a surface. We also show that for covering 2-groups the surface holonomy of any connection taking values in a torus computes an invariant of the bundle. Roughly the first half of the thesis is dedicated to a comprehensive introduction to gauge theory and 2-category theory before proceeding to 2-gauge theory. | |
dc.description.sponsorship | Utrecht University | |
dc.format.extent | 684490 | |
dc.format.mimetype | application/pdf | |
dc.language.iso | en | |
dc.title | Higher Gauge Theory | |
dc.type.content | Master Thesis | |
dc.rights.accessrights | Open Access | |
dc.subject.keywords | Mathematical Physics; Gauge Theory; Category Theory | |
dc.subject.courseuu | Mathematical Sciences |