Towards the study of the metric properties of the new fuzzy spheres of Fiore and Pisacane

Noncommutative spaces are strong candidates for the description of the underlying quantum structure of spacetime, and in this document we can see them arise through the introduction of energy cut-offs in a quantum theory. The purpose of this document is to develop a basic understanding of the geometry of noncommutative spaces that may arise in physically plausible situations such as those derived from the introduction of such cut-offs. In order to do this, we first study the traditional fuzzy sphere of Madore and its metric properties. We then embark on the research of the geometry of the fuzzy spheres recently proposed by Fiore and Pisacane through energy cut-offs by studying their definition and equivalent characterizations, as well as some systems of coherent states on them, which play the role of points on these noncommutative spheres, and which enable the use of these spaces in areas outside of geometry. Consequently, we provide the mathematical basis for the study of (yet to be constructed) spectral triples on these spaces, as well as the metric structure they will induce.

• Autores: Puerto Galindo, Sebastian Camilo
• Tipo de recurso: Trabajo de grado de pregrado
• Fecha de publicación: 2021
• Institución: Universidad de los Andes
• Repositorio: Séneca: repositorio Uniandes
• Idioma: spa
• OAI Identifier: oai:repositorio.uniandes.edu.co:1992/54996
• Acceso en línea: http://hdl.handle.net/1992/54996
• Palabra clave: Espacios noconmutativos; Estructura cuántica subyacente; Espacio-tiempo; Teoría cuántica; Energías de corte; Física
• Rights: openAccess
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/