Publication: Cosmología cuántica de lazos y campo fermiónicos
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2018-05-21
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Universidad Complutense de Madrid
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Abstract
La Teoría Cuántica de Campos (TCC) en espacio tiempos curvos está sujeta a una ambiguedad inherente que permite una libertad innata a la hora de elegir el vac o, incluso para descripciones de Fock de campos libres. Sobre fondos no estacionarios, esta ambiguedad no puede eliminarse, en general, mediante consideraciones de simetría. A su vez, es habitual que la no estacionariedad del fondo suponga una seria obstrucción a la implementabilidad unitaria de la dinámica del campo. Esta situación plantea un grave problema si queremos que la teoría cuántica mantenga su interpretación probabilística usual, y por ende la coherencia en la evolución. Afortunadamente, para campos escalares libres en espacio tiempos conformemente ultrastáticos, como son los que describen las cosmologías homogéneas e isótropas, se ha demostrado recientemente que el requisito de una implementabilidad unitaria de la dinámica, junto con la invariancia de las estructuras cuánticas bajo las simetrías del sistema, garantizan la unicidad de la cuantización de Fock (salvo transformaciones unitarias). Es de enorme interés extender estos resultados de unicidad a otro tipo de campos que puedan describir un contenido material mas realista del Universo como, por ejemplo, campos fermiónicos. En esta tesis, abordamos con éxito este problema para el campo de Dirac, demostrando la unicidad de su representación de Fock bajo nuestro criterio de unitariedad dinámica e invariancia frente a las simetrías físicas. Probamos esta unicidad en dos escenarios diferentes. El primero es un campo de Dirac en espacio tiempos conformemente ultrastáticos de tres dimensiones, con aplicaciones en materia condensada...
Quantum Field Theory (QFT) in curved spacetimes is subject to an inherent ambiguity that allows for an in nite freedom in the choice of vacuum, even for free eld Fock descriptions. In non-stationary backgrounds, this ambiguity cannot be eliminated, in general, by symmetry considerations. In turn, it is common that the non-stationarity of the background entails a serious obstruction to the unitary implementability of the eld dynamics. This situation poses a fundamental problem if one wants to maintain the usual probabilistic interpretation of Quantum Mechanics, and hence coherence in the quantum evolution. Fortunately, for free scalar elds in conformally ultrastatic spacetimes, such as those describing homogeneous and isotropic cosmologies, it has recently been shown that the requirement of a unitary implementation of the dynamics, together with the invariance of the quantum structures under the symmetries of the system, guarantees the uniqueness of the Fock quantization (modulo unitary transformations). It is of the greatest interest extending these uniqueness results to other elds that can describe more realistic matter content in the Universe, such as fermion els. In this thesis, we successfully address this problem for the Dirac eld, demonstrating the uniqueness of its Fock representation under our criterion of unitarity of the dynamics and invariance under the physical symmetries. We prove this uniqueness in two di erent scenarios. The rst one is a Dirac eld in three-dimensional conformally ultrastatic spacetimes, with applications in condensed matter theory...
Quantum Field Theory (QFT) in curved spacetimes is subject to an inherent ambiguity that allows for an in nite freedom in the choice of vacuum, even for free eld Fock descriptions. In non-stationary backgrounds, this ambiguity cannot be eliminated, in general, by symmetry considerations. In turn, it is common that the non-stationarity of the background entails a serious obstruction to the unitary implementability of the eld dynamics. This situation poses a fundamental problem if one wants to maintain the usual probabilistic interpretation of Quantum Mechanics, and hence coherence in the quantum evolution. Fortunately, for free scalar elds in conformally ultrastatic spacetimes, such as those describing homogeneous and isotropic cosmologies, it has recently been shown that the requirement of a unitary implementation of the dynamics, together with the invariance of the quantum structures under the symmetries of the system, guarantees the uniqueness of the Fock quantization (modulo unitary transformations). It is of the greatest interest extending these uniqueness results to other elds that can describe more realistic matter content in the Universe, such as fermion els. In this thesis, we successfully address this problem for the Dirac eld, demonstrating the uniqueness of its Fock representation under our criterion of unitarity of the dynamics and invariance under the physical symmetries. We prove this uniqueness in two di erent scenarios. The rst one is a Dirac eld in three-dimensional conformally ultrastatic spacetimes, with applications in condensed matter theory...
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Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Físicas, leída el 26-06-2017