Extended objects in quantum field theory in three dimensions and applications
In this thesis the systematic study of Quantum Field Theories (QFT) in various dimensions is proposed from the point of view of mathematical and theoretical physics, paying special attention to systems of one and three spatial dimensions (in addition to the temporal dimension in both cases) under th...
| Autor: | |
|---|---|
| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad de Valladolid |
| Repositorio: | UVaDOC. Repositorio Documental de la Universidad de Valladolid |
| OAI Identifier: | oai:uvadoc.uva.es:10324/59757 |
| Acceso en línea: | https://doi.org/10.35376/10324/59757 https://uvadoc.uva.es/handle/10324/59757 |
| Access Level: | acceso abierto |
| Palabra clave: | Física Quantum field theory Theoretical physics Física teórica Mathematical physics Física matemática Quantum physics Física cuántica 2212 Física Teórica |
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Extended objects in quantum field theory in three dimensions and applications |
| title |
Extended objects in quantum field theory in three dimensions and applications |
| spellingShingle |
Extended objects in quantum field theory in three dimensions and applications Santamaría Sanz, Lucía Física Quantum field theory Theoretical physics Física teórica Mathematical physics Física matemática Quantum physics Física cuántica 2212 Física Teórica |
| title_short |
Extended objects in quantum field theory in three dimensions and applications |
| title_full |
Extended objects in quantum field theory in three dimensions and applications |
| title_fullStr |
Extended objects in quantum field theory in three dimensions and applications |
| title_full_unstemmed |
Extended objects in quantum field theory in three dimensions and applications |
| title_sort |
Extended objects in quantum field theory in three dimensions and applications |
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Santamaría Sanz, Lucía |
| author |
Santamaría Sanz, Lucía |
| author_facet |
Santamaría Sanz, Lucía |
| author_role |
author |
| dc.contributor.none.fl_str_mv |
Nieto Calzada, Luis Miguel Muñoz Castañeda, José María Universidad de Valladolid. Escuela de Doctorado |
| dc.subject.none.fl_str_mv |
Física Quantum field theory Theoretical physics Física teórica Mathematical physics Física matemática Quantum physics Física cuántica 2212 Física Teórica |
| topic |
Física Quantum field theory Theoretical physics Física teórica Mathematical physics Física matemática Quantum physics Física cuántica 2212 Física Teórica |
| description |
In this thesis the systematic study of Quantum Field Theories (QFT) in various dimensions is proposed from the point of view of mathematical and theoretical physics, paying special attention to systems of one and three spatial dimensions (in addition to the temporal dimension in both cases) under the influence of some particular external conditions. These conditions vary from local interactions with other external classical fields to ideal boundary conditions in confining geometries. More specifically, the main objective of this work is the study of the spectrum of quantum fluctuations of the fields in the vacuum state subject to the external conditions indicated. This study will be applied to the calculation of several relevant parameters in three-dimensional and one-dimensional extended structures. These systems have recently received increasing interest in material physics (in micro-electromechanical devices based on the Casimir effect or topological defects in metamaterials and nanotubes) and in fundamental physics (quantum effects in modern cosmology and topological defects such as domain walls, monopoles and skyrmions). Different configurations of quantum fields both in compact domains and in open ones with boundaries will be studied: -A scalar field confined between plates mimicked by the most general type of lossless and frequently independent boundary conditions. -Scalar fields propagating at finite temperature under the influence of generalised Dirac delta lattices and Pöschl-Teller combs. -Scalar fields between two parallel plates mimicked by Dirac delta potentials in a curved background of a topological Pöschl-Teller kink. -Relativistic fermionic particles propagating in the real space under the influence of either a single and a double Dirac delta potential. Only effective theories will be considered. Here effective means that the microscopic degrees of freedom relative to the atoms and quarks of the matter composing the plates or objects between which the vacuum quantum interaction energy will be studied are not going to be taken into account. The methodology developed for the project is the following. Firstly, the spectrum of the non-relativistic Schrödinger operator or the relativistic Dirac one that will give rise to the set of one-particle states of the corresponding QFT will be characterised. Secondly, analytical and numerical results of the vacuum interaction energy between extended objects at zero temperature will be obtained. Finally, the study will be generalised to other thermodynamic magnitudes of interest such as the one loop quantum corrections to the Helmholtz free energy, the entropy and the Casimir force between objects at finite non zero temperature. Furthermore, graphical representations obtained numerically with the software Mathematica will be added. The thesis is structured in such a way that Chapter 1 gives an introduction to the work as a whole and the following chapters present the concrete results of each of the systems listed above. Finally, Chapter 6 summarises the main conclusions to give an overall view of the work carried out. |
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2023 |
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2023 |
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https://doi.org/10.35376/10324/59757 https://uvadoc.uva.es/handle/10324/59757 |
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https://doi.org/10.35376/10324/59757 https://uvadoc.uva.es/handle/10324/59757 |
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info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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Extended objects in quantum field theory in three dimensions and applicationsSantamaría Sanz, LucíaFísicaQuantum field theoryTheoretical physicsFísica teóricaMathematical physicsFísica matemáticaQuantum physicsFísica cuántica2212 Física TeóricaIn this thesis the systematic study of Quantum Field Theories (QFT) in various dimensions is proposed from the point of view of mathematical and theoretical physics, paying special attention to systems of one and three spatial dimensions (in addition to the temporal dimension in both cases) under the influence of some particular external conditions. These conditions vary from local interactions with other external classical fields to ideal boundary conditions in confining geometries. More specifically, the main objective of this work is the study of the spectrum of quantum fluctuations of the fields in the vacuum state subject to the external conditions indicated. This study will be applied to the calculation of several relevant parameters in three-dimensional and one-dimensional extended structures. These systems have recently received increasing interest in material physics (in micro-electromechanical devices based on the Casimir effect or topological defects in metamaterials and nanotubes) and in fundamental physics (quantum effects in modern cosmology and topological defects such as domain walls, monopoles and skyrmions). Different configurations of quantum fields both in compact domains and in open ones with boundaries will be studied: -A scalar field confined between plates mimicked by the most general type of lossless and frequently independent boundary conditions. -Scalar fields propagating at finite temperature under the influence of generalised Dirac delta lattices and Pöschl-Teller combs. -Scalar fields between two parallel plates mimicked by Dirac delta potentials in a curved background of a topological Pöschl-Teller kink. -Relativistic fermionic particles propagating in the real space under the influence of either a single and a double Dirac delta potential. Only effective theories will be considered. Here effective means that the microscopic degrees of freedom relative to the atoms and quarks of the matter composing the plates or objects between which the vacuum quantum interaction energy will be studied are not going to be taken into account. The methodology developed for the project is the following. Firstly, the spectrum of the non-relativistic Schrödinger operator or the relativistic Dirac one that will give rise to the set of one-particle states of the corresponding QFT will be characterised. Secondly, analytical and numerical results of the vacuum interaction energy between extended objects at zero temperature will be obtained. Finally, the study will be generalised to other thermodynamic magnitudes of interest such as the one loop quantum corrections to the Helmholtz free energy, the entropy and the Casimir force between objects at finite non zero temperature. Furthermore, graphical representations obtained numerically with the software Mathematica will be added. The thesis is structured in such a way that Chapter 1 gives an introduction to the work as a whole and the following chapters present the concrete results of each of the systems listed above. Finally, Chapter 6 summarises the main conclusions to give an overall view of the work carried out.El objetivo de esta tesis es el estudio, bajo el punto de vista de la física matemática, de teorías cuánticas de campos (TCC) en una y en tres dimensiones espaciales (aparte de la temporal) bajo la influencia de diversas condiciones externas. Estas condiciones comprenden tanto la interacción con otros campos clásicos externos así como condiciones de borde en geometrías confinantes. En particular, el principal interés de este trabajo es el estudio del espectro de las fluctuaciones cuánticas de los campos en el estado de vacío sujeto a las condiciones externas anteriormente indicadas. Este estudio permitirá obtener parámetros relevantes en algunas estructuras extensas en una y tres dimensiones. Este tipo de sistemas han suscitado recientemente un gran interés en la física de materiales (por ejemplo en dispositivos microelectromecánicos basados en el efecto Casimir, nanotubos y defectos topológicos en metamateriales) y en física fundamental (defectos topológicos como paredes de dominio, cuerdas cósmicas, monopolos y skyrmiones). A lo largo de la tesis se van a estudiar las diferentes configuraciones de campos cuánticos, tanto en dominios compactos como en dominios abiertos con bordes, que se enumeran a continuación: -Campos escalares confinados entre placas representadas por las condiciones de contorno independientes de las frecuencias más generales posibles. -Campos escalares que se propagan a temperatura finita bajo la influencia de redes de tipo delta de Dirac generalizadas y peines formados con potenciales Pöschl-Teller. -Campos escalares en un sistema formado por dos placas paralelas modelizadas por potenciales delta de Dirac introducidas en un potencial de fondo curvo dado por un kink topológico de tipo sine-Gordon. -Partículas fermiónicas relativistas que se propagan en el espacio real bajo la influencia de tanto uno como varios potenciales delta de Dirac. Es importante destacar que en esta tesis se van a considerar únicamente teorías ”efectivas”, en el sentido de que no se van a tener en cuenta los grados de libertad microscópicos relativos a los átomos y los quarks de la materia que compone las placas o objetos entre los cuales se va a estudiar la energía de interacción cuántica de vacío. La metodología general empleada para la obtención de estos objetivos es la siguiente: primero se caracterizará el espectro del operador de Schrödinger no relativista que dará lugar al conjunto de estados de una partícula de la teoría cuántica de campos correspondiente, después se obtendrán fórmulas analíticas para el cálculo de la energía de vacío de interacción entre los objetos extensos considerados a temperatura cero y finalmente se generalizará el estudio a otras magnitudes termodinámicas de interés como las correcciones cuánticas a un lazo de la energía libre de Helmholtz, la entropía y la fuerza de Casimir entre los objetos a temperatura finita no nula. Se obtendrán resultados analíticos cuando sea posible y además, todo ello irá acompañado de representaciones gráficas obtenidas numéricamente con ayuda del software Mathematica. La tesis está organizada de forma que el primer capítulo es una introducción bibliográfica al trabajo en su conjunto y los siguientes capítulos presentan los resultados concretos de cada uno de los sistemas anteriormente enumerados. Finalmente, el capítulo 6 resume las principales conclusiones de la tesis para dar una visión global del trabajo realizado.Escuela de DoctoradoDoctorado en FísicaNieto Calzada, Luis MiguelMuñoz Castañeda, José MaríaUniversidad de Valladolid. Escuela de Doctorado2023info:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://doi.org/10.35376/10324/59757https://uvadoc.uva.es/handle/10324/59757reponame:UVaDOC. Repositorio Documental de la Universidad de Valladolidinstname:Universidad de ValladolidInglésinfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-nd/4.0/oai:uvadoc.uva.es:10324/597572026-06-13T12:44:47Z |
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15,300724 |