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...
- 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/
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Al consultar y hacer uso de este recurso, está aceptando las condiciones de uso establecidas por los autores.http://creativecommons.org/licenses/by-nc-sa/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Winklmeier, Monika Anna081ebbb8-d1c1-4112-b949-6f6d13317e2c400Sánchez Mendoza, Daniel63ada97c-c7e2-456e-9fc3-94bb2820c95d400Cortissoz Iriarte, Jean Carlos2022-09-26T22:34:23Z2022-09-26T22:34:23Z2017http://hdl.handle.net/1992/61733instname:Universidad de los Andesreponame:Repositorio Institucional Sénecarepourl:https://repositorio.uniandes.edu.co/795479-1001"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."El objetivo de este trabajo es probar la existencia de valores propios de una familia de operadores de Dirac. Dado que estos operadores no son semiacotados el principio variacional clásico no aplica directamente. En el caso de masa constante, el principio variacional clásico puede aplicarse al cuadrado del operador, dando lugar a condiciones para la existencia de valores propios en el gap espectral. En el caso de masa no constante este método no funciona y tenemos que aplicar un Principio Variacional Generalizado que permita de nuevo derivar criterios para la existencia de valores propios el gap espectral." -- Tomado del Formato de Documento de Grado.MatemáticoPregrado31 hojasapplication/pdfengUniversidad de los AndesMatemáticasFacultad de CienciasDepartamento de MatemáticasOn dirac operators and variational principlesTrabajo de grado - Pregradoinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_7a1fTexthttp://purl.org/redcol/resource_type/TPEcuaciones diferenciales parcialesEcuación de DiracOperadores diferencialesPrincipios variacionalesTeoría del campo cuántico201125252PublicationTHUMBNAIL13299.pdf.jpg13299.pdf.jpgIM Thumbnailimage/jpeg6390https://repositorio.uniandes.edu.co/bitstreams/4b8ca09f-80db-4f28-9120-b434bc0c33e4/downloaddd94916d251d866f2019b0a063fd9099MD53ORIGINAL13299.pdfapplication/pdf383675https://repositorio.uniandes.edu.co/bitstreams/048eb3b6-8612-4787-bdf8-b5e7468db173/downloadae8295ed729fdc220706a8aaf644745aMD51TEXT13299.pdf.txt13299.pdf.txtExtracted texttext/plain48914https://repositorio.uniandes.edu.co/bitstreams/c5b4cfc1-1b8f-4133-9537-ba493d60e579/download8110e506ed9e4c0766516f724f9b664cMD521992/61733oai:repositorio.uniandes.edu.co:1992/617332023-10-10 17:01:36.15http://creativecommons.org/licenses/by-nc-sa/4.0/open.accesshttps://repositorio.uniandes.edu.coRepositorio institucional Sénecaadminrepositorio@uniandes.edu.co |
| dc.title.spa.fl_str_mv |
On dirac operators and variational principles |
| title |
On dirac operators and variational principles |
| spellingShingle |
On dirac operators and variational principles Ecuaciones diferenciales parciales Ecuación de Dirac Operadores diferenciales Principios variacionales Teoría del campo cuántico |
| title_short |
On dirac operators and variational principles |
| title_full |
On dirac operators and variational principles |
| title_fullStr |
On dirac operators and variational principles |
| title_full_unstemmed |
On dirac operators and variational principles |
| title_sort |
On dirac operators and variational principles |
| dc.creator.fl_str_mv |
Sánchez Mendoza, Daniel |
| dc.contributor.advisor.none.fl_str_mv |
Winklmeier, Monika Anna |
| dc.contributor.author.none.fl_str_mv |
Sánchez Mendoza, Daniel |
| dc.contributor.jury.none.fl_str_mv |
Cortissoz Iriarte, Jean Carlos |
| dc.subject.keyword.spa.fl_str_mv |
Ecuaciones diferenciales parciales Ecuación de Dirac Operadores diferenciales Principios variacionales Teoría del campo cuántico |
| topic |
Ecuaciones diferenciales parciales Ecuación de Dirac Operadores diferenciales Principios variacionales Teoría del campo cuántico |
| description |
"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. |
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2017 |
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2017 |
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Universidad de los Andes |
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