Principal bundles, holonomy groups, and the Ambrose-Singer theorem
This thesis is devoted to review the theory of fiber bundles and principal bundles, and state and prove the Ambrose--Singer theorem. This result establishes the relationship between the holonomy group associated to a connection on a principal bundle and the curvature form of the connection. The theo...
| Autor: | |
|---|---|
| Tipo de documento: | dissertação |
| Data de publicação: | 2024 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositório: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglês |
| OAI Identifier: | oai:upcommons.upc.edu:2117/416474 |
| Acesso em linha: | https://hdl.handle.net/2117/416474 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Lie groups Lie algebras Fiber bundles Principal bundles Connections Holonomy Ambrose--Singer theorem Gauge and Yang--Mills theories Lie, Grups de Classificació AMS::22 Topological groups, lie groups::22E Lie groups Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Resumo: | This thesis is devoted to review the theory of fiber bundles and principal bundles, and state and prove the Ambrose--Singer theorem. This result establishes the relationship between the holonomy group associated to a connection on a principal bundle and the curvature form of the connection. The theory of connection forms in principal bundles has important applications in physics; in particular, in gauge and Yang--Mills theories. |
|---|