Giulini, Domenico
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Giulini, Domenico
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Giulini, Domenico
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Nico
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Item-typ:Veröffentlichung, Hamiltonian study of the asymptotic symmetries of gauge theories(2021-08-26); ; ; Asymptotic symmetries are a general and important feature of theories with long-ranging fields, such as gravity, electromagnetism, and Yang-Mills. They appear in the formalism once the analytic behaviour of fields near infinity is specified and have received a renewed interest in the last years after a possible connection with the information-loss paradox has been conjectured. One of the various methods used to study the asymptotic symmetries of field theories relies on the Hamiltonian formalism and was introduced in the seminal work of Henneaux and Troessaert, who successfully applied it to the case of gravity and electrodynamics, thereby deriving the respective asymptotic symmetry groups of these theories. The main advantage of this approach is that the study of the asymptotic symmetries ensues from clear-cut first principles. These include the minimal assumptions that are necessary to ensure the existence of Hamiltonian structures (phase space, symplectic form, differentiable Hamiltonian) and, in case of Poincaré invariant theories, a canonical action of the Poincaré group. In this thesis, after an extensive review of how the Hamiltonian approach to study asymptotic symmetries of gauge theories works, we apply these methods to two specific situations of physical interest. First, we deal with the non-abelian Yang-Mills case and we show that the above principles lead to trivial asymptotic symmetries (nothing else than the Poincaré group) and, as a consequence, to a vanishing total colour charge. This is a new and somewhat unexpected result. It implies that no globally colour-charged states exist in classical non-abelian Yang-Mills theory. The second situation considered in this thesis is a scalar field minimally-coupled to an abelian gauge field, which can be used to study, at the same time, two specific cases: scalar electrodynamics and the abelian Higgs model. We show that the situation in scalar electrodynamics amply depends on whether the scalar field is massive or massless, insofar as, in the latter case, one cannot canonically implement asymptotic symmetries. Furthermore, we illustrate that, in the abelian Higgs model, the asymptotic canonical symmetries reduce to the Poincaré group in an unproblematic fashion.Dissertation275 477 - Some of the metrics are blocked by yourconsent settings
Item-typ:Veröffentlichung, Deformation and Contraction of Symmetries in Special Relativity(2017-05-08); ; ; This dissertation gives an account of the fundamental principles underlying two conceptionally different ways of embedding Special Relativity into a wider context. Both of them root in the attempt to explore the full scope of the Relativity Postulate. The first approach uses Lie algebraic analysis alone, but already yields a whole range of alternative kinematics that are all in a quantifiable sense near to those in Special Relativity, while being rather far away in a qualitative way. The corresponding models for spacetime are seen to be four-dimensional versions of the prototypical planar geometries associated with the work of Cayley and Klein. The close relationship between algebraic and geometric methods displayed by these considerations is being substantialized in terms of light-like spacetime extensions. The second direction of departures from Special Relativity stresses and develops the algebraic view on spacetime by considering Hopf instead of Lie algebras as candidates for the description of kinematical transformations and hence spacetime symmetry. This approach is motivated by the belief in the existence of a quantum theory of gravity, and the assumption that such manifests itself in nonlinear modifications of the laws of Special Relativity at length scales comparable to the Planck length. The twofold character of this work, and the presentation of an example for the fully geometric character of a specific Hopf algebraic deformation of the PoincareI algebra, enable a conclusion that speculates on a possible relationship between the two developed viewpoints via the technique of nonlinear realizations. A non-perturbative approach to the latter is given which generalizes to all the considered geometries.Dissertation467 405 - Some of the metrics are blocked by yourconsent settings
Item-typ:Veröffentlichung, The Hawking Energy in cosmolgy(2021-06-15); ; ; Eine strikt auf Beobachtungen basierende Formulierung der Kosmologie basiert auf Lichtkegeln, die die kausale Struktur der Raumzeit respektieren. Der Rückwärtslichtkegel eines gegebenen Raumzeitpunktes ist die eindeutige und natürliche geometrische Struktur, die direkt mit kosmologischen Beobachtungen verbunden ist. In dieser Arbeit wird das Konzept einer Lichtkegelformulierung der Kosmologie mit der Suche nach einer Energiedefinition für das Gravitationsfeld in der Frage nach der Energie des beobachtbaren Universums und seiner Anwendungen im kosmologischen Kontext zusammengeführt. Diese Arbeit untersucht die Eigenschaften der Hawking’schen quasilokalen Energie auf dem Rückwärtslichtkegel eines kosmologischen Beobachters. Durch die Zerteilung des Lichtkegels in eine einparametrige Familie von Lichtkegelschnitten kann die Entwicklung der Hawkingenergie entlang des Lichtkegels untersucht werden. Im Regime schwacher Gravitation können Positivitäts- und Monotonieergebnisse etabliert werden. Hingegen führen starke Gravitationslinseneffekte dazu, dass sich der Lichtkegel selbst schneidet und Kaustiken präsent sind. In diesem Fall bleiben die Hawkingenergie und ihre Variation entlang der Nullgeneratoren des Lichtkegels in der Gegenwart von Schwalbenschwanz-Singularitäten zwar wohldefiniert, allerdings hängt das Monotonieverhalten von den Details der ein- und ausgehenden Beiträge ab. In einem zweiten Teil werden explizite kosmologische Anwendungen der Hawkingenergie, sowohl in einem inhomogenen, als auch einem FLRW Kontext präsentiert. Im inhomogenen Kontext wird gezeigt, dass für alle zweidimensionalen, nicht gefangenen Sphären mit gegebener Oberfläche und Durchschnittsdichte eine Materieverteilung ohne Nullscherung bei hinreichend hohen Dichten die Hawkingenergie maximiert. Des Weiteren kann die Hawkingenergie genutzt werden, um für jeden Lichtkegelschnitt ein Robertson-Walker Referenzschnitt gleicher Energie und Oberfläche zu konstruieren. Im FLRW Kontext wird die Energie konkret für räumlich flache FLRW Raumzeiten berechnet und anhand der Monotonie Schranken für die Dichte und die Zustandsgleichung des kosmischen Fluids abgeleitet.Dissertation321 297 - Some of the metrics are blocked by yourconsent settings
Item-typ:Veröffentlichung, Multi-Black-Hole Configurations as Models for Inhomogeneous Cosmologies(2017-05-09); ; ; On the largest scales, the Universe is homogeneous and isotropic, whereas on smaller scales, various structures immediately begin to emerge. The transition from an inhomogeneous spacetime to the homogeneous and isotropic Friedmann universe is not sufficiently understood yet. Modern cosmology rests on the hypothesis that the LambdaCDM-model applies and, indeed, this model is very successful. On the other hand, as the precision of observations steadily increases, it is more than likely that inhomogeneities will no longer be negligible in the future. For this reason, the study of inhomogeneous cosmological models is reasonable. In this thesis, we consider the question which Friedmann universe is the best fit to a particular given inhomogeneous spacetime, which is known as the fitting problem. We consider models in which matter is replaced by a discrete configuration of black holes, that is, we concentrate on vacuum solutions to Einstein's equations. Since the full system of the field equations is too complicated to find an exact time-dependent solution for the whole spacetime, we restrict ourselves to approximative models as well as solutions to the initial value problem. In the former case, we reconsider Swiss-cheese and Lindquist-Wheeler models. In both models, the spacetime around a mass is described by the Schwarzschild metric. In the latter case, we determine the spatial metric of a space-like hypersurface. We limit our attention to time-symmetric initial data characterised by the vanishing of the extrinsic curvature. In this case, we are able to find a solution for an arbitrary number of black holes using the conformal method. Clearly, it is not reasonable to assume that every configuration of black holes leads to a spacetime which may be approximated well by a Friedmann solution. Such an approximation should be possible if the masses are distributed somehow uniformly. The aim of this thesis is to clarify this statement and to provide criteria which allow quantitative statements about the degree of uniformity. We determine the parameters of the fitted dust universe, in particular the scale factor. Our considerations are supported by several example configurations. In particular, we provide a new method based on Lie sphere geometry to construct various configurations with a high degree of uniformity in a surprisingly simple fashion. Moreover, we provide a generalisation to an approximative inhomogeneous model given by Lindquist and Wheeler. In this case, it is possible to determine the parameters of the fitted Friedmann universe even if we do not know the exact solution. Under certain conditions, this model becomes similar to a Swiss-cheese model, allowing us to formulate first expectations on the time evolution, which is otherwise mostly disregarded within the framework of this thesis.Dissertation363 191