On dirac operators and variational principles

"The aim of this work is to prove the existence of eigenvalues of a family of Dirac operators. Since these operators are not semibounded the classical variational principle does not apply directly. In the case of constant mass the classical variational principle can be applied to the square of the operator, leading to conditions for existence of eigenvalues in the spectral gap. In the case of non constant mass this approach does not work and we have to apply a Generalized Variational Principle which again allows to derive criteria for the existence of eigenvalues in the spectral gap." -- Tomado del Formato de Documento de Grado.

• Autores: Sánchez Mendoza, Daniel
• Tipo de recurso: Trabajo de grado de pregrado
• Fecha de publicación: 2017
• Institución: Universidad de los Andes
• Repositorio: Séneca: repositorio Uniandes
• Idioma: eng
• OAI Identifier: oai:repositorio.uniandes.edu.co:1992/61733
• Acceso en línea: http://hdl.handle.net/1992/61733
• Palabra clave: Ecuaciones diferenciales parciales; Ecuación de Dirac; Operadores diferenciales; Principios variacionales; Teoría del campo cuántico
• Rights: openAccess
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/