Teorías gauge y gravedad de Chern-Simons en 2+1 dimensiones

Se estudian las teorías de gauge en el lenguaje abstracto de la Geometría Diferencial. Esto incluye: Grupos de Lie, acciones, brados, conexiones, curvaturas, etc. Estos temas se cubren a lo largo de las primeras secciones con la intención de servir como una introducción. Después, el objetivo principal es presentar numerosos ejemplos, con el mayor nivel de detalle permitido. Se analiza el electromagnetismo, comenzando por la libertad clásica de escoger los potenciales de la teoría. Tras ello, esta se describe en términos de U(1)- brados principales. Se estudian tambi én los monopolos de Dirac, que sirven como ejemplo de teor as con brados no triviales. El eletromagnetismo se generaliza a la teoría de Yang-Mills y se discuten las condiciones para la existencia una acción adecuada. El objetivo del último capítulo es introducir la gravedad de Chern-Simons en 2+1 dimensiones como teoría de gauge. En este caso, la teoría queda descrita en términos del vierbein, la conexión de Lorentz y el grupo de Poincaré, que es el grupo de simetrías de la misma.Gauge theories are studied in the abstract framework of Differential Geometry. This includes: Lie groups, actions, bre bundles, connections, curvatures, etc. These topics are covered throughout the rst sections with the intention to serve as an introduction. After that, the main focus is to present numerous examples, with the highest amount of detail posible. Electromagnetism is analyzed, starting with classical freedom to chose the electromagnetic potencial. Thereafter, the theory is described in terms of U(1)-principal bundles. Dirac monopoles are also studied, providing an example of a case where bre bundles are non-trivial. Electromagnetic theory is generalized to Yang-Mills theories and the conditions for the existence of such theories is examinated. The aim of the last chapter is to introduce gravity in 2+1 dimensions with a Chern-Simons action as a gauge theory. In this case, the theory is discribed in terms of the bundle of frames, the Lorentz connection and the Poincaré Group being the symmetry group for the theory.Grado en Físic

Formulación matemática de las teorías de gauge: grupos de Lie, teoría de representaciones, acciones de grupo, fibrados, conexión, curvatura y derivada covariante, aplicaciones físicas

La memoria está pensada como un trabajo coordinado con el Grado en Física. En este trabajo, se tratan las teorías de gauge desde el marco abstracto de la Geometría Diferencial. Esto incluye el estudio de: grupos de Lie, sus representaciones y sus acciones, fibrados principales, conexiones, curvaturas, derivadas covariantes, etc. Se presentan los resultados principales de manera rigurosa y con demostraciones. También se tratan algunos ejemplos, como el electromagnetismo o los monopolos de Dirac.Grado en Matemática

Healthcare workers hospitalized due to COVID-19 have no higher risk of death than general population. Data from the Spanish SEMI-COVID-19 Registry

Aim To determine whether healthcare workers (HCW) hospitalized in Spain due to COVID-19 have a worse prognosis than non-healthcare workers (NHCW). Methods Observational cohort study based on the SEMI-COVID-19 Registry, a nationwide registry that collects sociodemographic, clinical, laboratory, and treatment data on patients hospitalised with COVID-19 in Spain. Patients aged 20-65 years were selected. A multivariate logistic regression model was performed to identify factors associated with mortality. Results As of 22 May 2020, 4393 patients were included, of whom 419 (9.5%) were HCW. Median (interquartile range) age of HCW was 52 (15) years and 62.4% were women. Prevalence of comorbidities and severe radiological findings upon admission were less frequent in HCW. There were no difference in need of respiratory support and admission to intensive care unit, but occurrence of sepsis and in-hospital mortality was lower in HCW (1.7% vs. 3.9%; p = 0.024 and 0.7% vs. 4.8%; p<0.001 respectively). Age, male sex and comorbidity, were independently associated with higher in-hospital mortality and healthcare working with lower mortality (OR 0.211, 95%CI 0.067-0.667, p = 0.008). 30-days survival was higher in HCW (0.968 vs. 0.851 p<0.001). Conclusions Hospitalized COVID-19 HCW had fewer comorbidities and a better prognosis than NHCW. Our results suggest that professional exposure to COVID-19 in HCW does not carry more clinical severity nor mortality