Gauge theories on transitive Lie algebroids

The dynamics of the elementary particles of physics and their interactions are modeled by quantized gauge theories, a type of field theories. These include Quantum Electrodynamics, the Electroweak Interaction, Quantum Chromodynamics and the Standard Model of particle physics, which describe three of the four known fundamental forces and which classify all observed fundamental particles. The mathematical framework usually used for the formulation of gauge theories, prior to quantization, is that of the differential geometry of principal fiber bundles and vector bundles. In this document we study the use of the structure of transitive Lie algebroids as the mathematical framework for a possible generalization of the formulation of a gauge theory through an action functional: the integral of a differential form on the algebroid. From this, the standard formulation is derived as a particular case in which the underlying algebroid is the Atiyah Lie algebroid associated to the corresponding principal bundle.

• Autores: Puerto Galindo, Sebastián Camilo
• Tipo de recurso: Trabajo de grado de pregrado
• Fecha de publicación: 2020
• Institución: Universidad de los Andes
• Repositorio: Séneca: repositorio Uniandes
• Idioma: eng
• OAI Identifier: oai:repositorio.uniandes.edu.co:1992/51300
• Acceso en línea: http://hdl.handle.net/1992/51300
• Palabra clave: Campos de calibración (Física); Teoría de campos (Física); Algebroides de Lie; Geometría diferencial; Matemáticas
• Rights: openAccess
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/