Testé Lino, Eduardo (2018) Entropía de estrelazado en teoría de campos y holografía : aplicaciones al grupo de renormalización. / Entanglement eutropy in quantum field theory and hologaphy: aplications to the renormalization group. Tesis Doctoral en Física, Universidad Nacional de Cuyo, Instituto Balseiro.
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Resumen en español
En esta Tesis se estudian las Teorías Cuánticas de Campos y algunas de sus propiedades desde el punto de vista de la Teoría de la Información Cuántica. Especificamente, se estudia la entropía de entrelazado y la entropía relativa del vacío con el objetivo de su aplicación a la irreversibilidad del grupo de renormalización. El resultado principal es una prueba del Teorema A (irreveribilidad del grupo de renormaliación en dimensión espacio-temporal d = 4), como consecuencia de la subaditividad fuerte de la entropía de entrelazado del vacío, la invariancia de Lorentz y lo que hemos llamado la propiedad Markoviana del vacío. Demostramos esta última propiedad en detalle, que equivale a la saturación de la subaditividad fuerte de la entropía de von Neumann y a una identidad sobre los Hamiltonianos modulares de regiones con borde en el plano o el cono nulo. Se derivan expresiones explícitas y generales para los Hamiltonianos modulares y las entropías de von Neumann y de Rényi del vacío reducido a estas regiones. Esto nos permite ofrecer un cuadro unificado de los teoremas de irreversibilidad del grupo de renormalización en dimensión d = 2; 3; 4 como consecuencia de propiedades de la entropía de entrelazado del vacío de una Teoría Cuántica de Campos.
Resumen en inglés
In this Thesis we study Quantum Field Theories and some of its properties from the point of view of Quantum Information Theory. Especically, we study the entanglement entropy and relative entropy of the vacuum state with the goal of applying it to the irreversibility of the renormalization group. The main result is a proof of the Atheorem (irreversibility of the renormalization group in d = 4 space-time dimensions), as a consecuence of the strong subadditivity of entanglement entropy, Lorentz invariance and what we have called the Markov property of the vacuum state. We prove this last property in detail, which is equivalent to the saturation of the strong subadditivity of von Neumann entropy and a certain identity between the modular Hamiltonians of space-time regions with boundary on a null plane or a null cone. We obtain explicit and general expressions for the modular Hamiltonian, von Neumann and Renyi entropies for the vacuum state reduced to these regions. With this we are able to give a unied picture of the irreversibility theorems of the renormalization group in d = 2, 3, 4 dimensions as a consecuence of properties of the entanglement entropy of the vacuum of a Quantum Field Theory.
| Tipo de objeto: | Tesis (Tesis Doctoral en Física) |
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| Palabras Clave: | Quantum field theory; Teoría del campo cuántico; [Entanglement entropy; Entropía de entrelazado; Renormalization group; Grupo de renormalización; C theorems; Teorema C] |
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| Materias: | Física > Teoría de campos |
| Divisiones: | Gcia. de área de Investigación y aplicaciones no nucleares > Gcia. de Física > Sistemas complejos y altas energías > Partículas y campos |
| Código ID: | 715 |
| Depositado Por: | Tamara Cárcamo |
| Depositado En: | 05 Jun 2019 15:04 |
| Última Modificación: | 05 Jun 2019 15:04 |
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