van der Velde , Guido G. (2024) Medidas de información en teoría cuántica de campos: hamiltonianos modulares y entropía para teorías incompletas / Information measures in quantum field theory: modular hamiltonians and entropy for incomplete theories. Tesis Doctoral en Física, Universidad Nacional de Cuyo, Instituto Balseiro.
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Resumen en español
En esta tesis se estudian dos problemas diferentes de teoría cuántica de campos utilizando herramientas de teoría de información. La primera parte se aboca al cálculo analítico de hamiltonianos modulares para teorías no conformes definidas en la semirrecta y que resultan de la reducción dimensional del escalar y el fermión libres no masivos. La estrategia utilizada consiste en reducir dimensionalmente el hamiltoniano modular en la d esfera para las teorías originales. El resultado se apoya en la factorización del estado reducido al segmento, asociando el flujo modular con simetrías de las teorías efectivas unidimensionales y endomorfismos en el desarrollo causal del intervalo. Resolviendo el espectro de los hamiltonianos modulares encontrados, que dependen del modo angular ℓ, se calcula analíticamente la entropía de entrelazamiento para el segmento. Si bien la suma sobre ℓ de estas entropías es divergente, se propuso un método de regularización novedoso que permite reproducir la estructura de divergencias para la entropía en la d esfera del escalar y el fermión libres. En particular, se logran reproducir los términos universales, representados por la anomalía tipo A en dimensión par arbitraria y la energía libre en la esfera euclídea F en d = 3, lo que resulta una mejora respecto de la regularización radial existente. La segunda parte de la tesis se enfoca en el modelo de Maxwell en 2 + 1 dimensiones. Más específicamente, en los problemas de asignación álgebra-legión característicos de teorías con simetrías generalizadas. En este sentido, se estudia el modelo en un marco dual representado por las derivadas del campo escalar libre. Además, aprovechando la simetría rotacional de las regiones consideradas, se reduce dimensionalmente el problema a la semirrecta, donde toda la diferencia entre el Maxwell y el escalar completo radica en el modo de Fourier n = 0. Así, en una red radial, se analiza la ruptura de la dualidad de Haag. Además, se calcula la entropía en el disco, mostrando que la contribución topológica resultante es inestable frente a distintas realizaciones en la red, con lo cual no es universal. También se calcula la información mutua entre un disco y su complemento, que sí es una cantidad independiente de la regularización. Separando la contribución de los operadores de twist que generan las simetrías generalizadas, se logró reproducir el doble logaritmo predicho en la literatura.
Resumen en inglés
In this thesis, two distinct problems in quantum field theory are addressed using information theory tools. The first part is devoted to the analytic calculation of modular Hamiltonians for non-conformal theories defined on the semi-infinite line, resulting from the dimensional reduction of massless free scalar and fermion fields. The approach involves dimensionally reducing the modular Hamiltonian on the d-sphere for the original theories. The results rely on the factorization of the reduced state in the segment, relating the modular flow with the symmetries of the effective one-dimensional the- ories and endomorphisms in the causal development of the interval. By solving the spectrum of the found modular Hamiltonians, which depend on the angular mode ℓ, the entanglement entropy for the segment is analytically calculated. Although the sum over ℓ of these entropies diverges, a novel regularization method was proposed that allows for the reproduction of the divergence structure for the entropy on the d-sphere of free scalars and fermions. In particular, the universal terms, represented by the type A anomaly in arbitrary even dimensions and the free energy on the Euclidean sphere F in d = 3, are successfully reproduced, which marks an improvement over existing radial regularization. The second part of the thesis focuses on the Maxwell model in 2 + 1 dimensions. More specifically, it addresses the algebra-region assignment problems characteristic of theories with generalized symmetries. In this context, the model is studied within a dual framework represented by the derivatives of the free scalar field. Leveraging the rotational symmetry of the considered regions, the problem is dimensionally reduced to the semi-infinite line, where the entire difference between Maxwell and the complete scalar lies in the Fourier mode n = 0. Thus, on a radial lattice, the breaking of Haag duality is analyzed. Furthermore, the entropy in the disk is calculated, showing that the resulting topological contribution is unstable against different lattice realizations, thereby lacking universality. The mutual information between a disk and its comple- ment, which is a regularization-independent quantity, is also calculated. By isolating the contribution of twist operators that generate generalized symmetries, the double logarithm predicted in the literature was successfully reproduced.
| Tipo de objeto: | Tesis (Tesis Doctoral en Física) |
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| Palabras Clave: | Hamiltonians; Hatiltonianos; Quantum field theory; Teoría del campo cuántico; [Modular hamiltonians; Hamiltonianos modulares; Generalized symmetries; Simetrias generalizadas; Haag duality; Dualidad de Haag; Maxwell theory; Teoría de Maxwell; Dimencional reduction; Reducción dimensional] |
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| Materias: | Física > Teoría cuántica 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: | 1257 |
| Depositado Por: | Tamara Cárcamo |
| Depositado En: | 13 Sep 2024 15:26 |
| Última Modificación: | 13 Sep 2024 15:26 |
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