Pontello, Diego E. (2019) Aspectos de la entropía de entrelazamiento en teoría algebraica de campos. / Aspects of entanglement entropy in algebraic quantum field theory. Tesis Doctoral en Física, Universidad Nacional de Cuyo, Instituto Balseiro.
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Resumen en español
En esta tesis, estudiamos aspectos de la entropía de entrelazamiento en teorías cuánticas de campos siguiendo un enfoque algebraico. La principal motivación del trabajo es explorar y comprender mejor la estructura general del entrelazamiento en teorías de campos relativistas, con el objetivo ultimo de buscar una formulación axiomática de la teoría cuántica de campos en términos de cantidades puramente entrópicas y elementos de la teoría de información. Por otro lado, también estamos interesados en explorar las consecuencias del entrelazamiento en teoría algebraica de campos, con el propósito de descubrir propiedades no conocidas de las teorías cuánticas de campos y entender aun mejor las ya conocidas. Esto nos ayudaría con el propósito de encontrar un "principio dinámico" que nos permita construir, de forma rigurosa, modelos no triviales de teorías de campos relativistas. Como veremos a lo largo de esta tesis, el enfoque algebraico es el esquema natural para definir y estudiar el entrelazamiento en teoría cuántica de campos, y por lo tanto, para plantear y realizar estas investigaciones. En los primeros capítulos de la tesis realizamos una revisión autocontenido de la teoría algebraica de campos y la teoría de información cuántica, mientras que en los capítulos finales nos centramos en los resultados obtenidos. Entre ellos, destacamos los cálculos, de forma matemáticamente rigurosa, de medidas de entrelazamiento y Hamiltonianos modulares para algunos modelos específicos de teorías de campos, usando técnicas de la teoría algebraica de campos y la teoría modular de algebras de von Neumann. Los resultados obtenidos nos muestran explícitamente aspectos no locales y universales de los Hamiltonianos modulares, y nos ayuda a resolver ambiguedades que aparecen cuando uno realiza cálculos similares usando técnicas y métodos no rigurosos. También estudiamos, de forma general, las consecuencias e implicancias de la entropía de entrelazamiento en teorías de campos que presentan una estructura no trivial de sectores de superselección proveniente de simetrías globales. Para esto seguimos el enfoque algebraico desarrollado por Doplicher, Haag y Roberts. Como resultado, encontramos un parámetro de orden entrópico que \mide" el tamaño del grupo de simetría y el cual esta formado por la diferencia de dos informaciones mutuas. Mas aun, logramos identificar, para una teoría de campos general, cuales son los operadores responsables de esta diferencia, y encontramos una relación desconocida (que involucra dichos operadores) de la teoría de información en teoría de campos: la relación de certidumbre entrópica. También argumentamos que esta relación puede ser extendida a contextos mas generales y mantiene una relación estrecha con la teoría de subfactores de algebras de von Neumann.
Resumen en inglés
In this thesis, we study aspects of entanglement theory of quantum field theories from an algebraic point of view. The main motivation is to gain insights about the general structure of the entanglement in QFT, towards a definition of an entropic version of QFT. In the opposite direction, we are also interested in exploring any consequence of the entanglement in algebraic QFT. This may help us to reveal unknown features of QFT, with the nal aim of nding a dynamical principle which allows us to construct non-trivial and rigorous models of QFT. The algebraic approach is the natural framework to dene and study entanglement in QFT, and hence, to pose the above inquiries. After a self-contained review of algebraic QFT and quantum information theory in operator algebras, we focus on our results. We compute, in a mathematically rigorous way, exact solutions of entanglement measures and modular Hamiltonians for specic QFT models, using algebraic tools from modular theory of von Neumann algebras. These calculations show explicitly non-local features of modular Hamiltonians and help us to solve ambiguities that arise in other non-rigorous computations. We also study aspects of entanglement entropy in theories having superselection sectors coming from global symmetries. We follow the algebraic perspective of Doplicher, Haag, and Roberts. In this way, we find an entropic order parameter that \measures" the size of the symmetry group, which is made out of a difference of two mutual informations. Moreover, we identify the main operators that take account of such a difference, and we obtain a new quantum information quantity, the entropic certainty relation, involving algebras containing such operators. This certainty relation keeps an intrinsic connection with subfactor theory of von Neumann algebras.
| Tipo de objeto: | Tesis (Tesis Doctoral en Física) |
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| Palabras Clave: | Information theory; Teoría de la información; Quantum information; Información cuántica; [Von Neumann algebras; Álgebras de Von Neumann; Quantum information theory; Teoría de información cuántica; Entanglement entropy; Entropía de entrelazamiento; Modular hamiltonians; Hamiltonianos modulares ] |
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| Materias: | Física |
| Divisiones: | Investigación y aplicaciones no nucleares > Física > Partículas y campos |
| Código ID: | 994 |
| Depositado Por: | Tamara Cárcamo |
| Depositado En: | 24 Ene 2022 10:01 |
| Última Modificación: | 24 Ene 2022 10:01 |
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