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Motiviert durch neuere Vorschläge zur experimentellen Untersuchung von Quantengravitationseffekten werden in der vorliegenden Arbeit Annahmen und Methoden untersucht, die für die Vorhersagen solcher Effekte im Rahmen der Loop-Quantengravitation verwendet werden können. Dazu wird als Modellsystem ein skalares Feld, gekoppelt an das Gravitationsfeld, betrachtet. <br /> Zunächst wird unter bestimmten Annahmen über die Dynamik des gekoppelten Systems eine Quantentheorie für das Skalarfeld vorgeschlagen. Unter der Annahme, dass sich das Gravitationsfeld in einem semiklassischen Zustand befindet, wird dann ein &quot;QFT auf gekrümmter Raumzeit-Limes&quot; dieser Theorie definiert. Im Gegensatz zur gewöhnlichen Quantenfeldtheorie auf gekrümmter Raumzeit beschreibt die Theorie in diesem Grenzfall jedoch ein quantisiertes Skalarfeld, das auf einem (klassisch beschriebenen) Zufallsgitter propagiert. <br /> Sodann werden Methoden vorgeschlagen, den Niederenergieliemes einer solchen Gittertheorie, vor allem hinsichtlich der resultierenden modifizierten Dispersonsrelation, zu berechnen. Diese Methoden werden anhand von einfachen Modellsystemen untersucht. <br /> Schließlich werden die entwickelten Methoden unter vereinfachenden Annahmen und der Benutzung einer speziellen Klasse von semiklassischen Zuständen angewandt, um Korrekturen zur Dispersionsrelation des skalaren und des elektromagnetischen Feldes im Rahmen der Loop-Quantengravitation zu berechnen. Diese Rechnungen haben vorläufigen Charakter, da viele Annahmen eingehen, deren Gültigkeit genauer untersucht werden muss. Zumindest zeigen sie aber Probleme und Möglichkeiten auf, im Rahmen der Loop-Quantengravitation Vorhersagen zu machen, die sich im Prinzip experimentell verifizieren lassen. / Motivated by recent proposals on the experimental detectability of quantum gravity effects, the present thesis investigates assumptions and methods which might be used for the prediction of such effects within the framework of loop quantum gravity. To this end, a scalar field coupled to gravity is considered as a model system. <br /> Starting from certain assumptions about the dynamics of the coupled gravity-matter system, a quantum theory for the scalar field is proposed. Then, assuming that the gravitational field is in a semiclassical state, a &quot;QFT on curved space-time limit&quot; of this theory is defined. In contrast to ordinary quantum field theory on curved space-time however, in this limit the theory describes a quantum scalar field propagating on a (classical) random lattice. <br /> Then, methods to obtain the low energy limit of such a lattice theory, especially regarding the resulting modified dispersion relations, are discussed and applied to simple model systems. <br /> Finally, under certain simplifying assumptions, using the methods developed before as well as a specific class of semiclassical states, corrections to the dispersion relations for the scalar and the electromagnetic field are computed within the framework of loop quantum gravity. These calculations are of preliminary character, as many assumptions enter whose validity remains to be studied more thoroughly. However they exemplify the problems and possibilities of making predictions based on loop quantum gravity that are in principle testable by experiment.

Which tensor fields G on a smooth manifold M can serve as a spacetime structure? In the first part of this thesis, it is found that only a severely restricted class of tensor fields can provide classical spacetime geometries, namely those that can carry predictive, interpretable and quantizable matter dynamics. The obvious dependence of this characterization of admissible tensorial spacetime geometries on specific matter is not a weakness, but rather presents an insight: it was Maxwell theory that justified Einstein to promote Lorentzian manifolds to the status of a spacetime geometry. Any matter that does not mimick the structure of Maxwell theory, will force us to choose another geometry on which the matter dynamics of interest are predictive, interpretable and quantizable. These three physical conditions on matter impose three corresponding algebraic conditions on the totally symmetric contravariant coefficient tensor field P that determines the principal symbol of the matter field equations in terms of the geometric tensor G: the tensor field P must be hyperbolic, time-orientable and energy-distinguishing. Remarkably, these physically necessary conditions on the geometry are mathematically already sufficient to realize all kinematical constructions familiar from Lorentzian geometry, for precisely the same structural reasons. This we were able to show employing a subtle interplay of convex analysis, the theory of partial differential equations and real algebraic geometry. In the second part of this thesis, we then explore general properties of any hyperbolic, time-orientable and energy-distinguishing tensorial geometry. Physically most important are the construction of freely falling non-rotating laboratories, the appearance of admissible modified dispersion relations to particular observers, and the identification of a mechanism that explains why massive particles that are faster than some massless particles can radiate off energy until they are slower than all massless particles in any hyperbolic, time-orientable and energy-distinguishing geometry. In the third part of the thesis, we explore how tensorial spacetime geometries fare when one wants to quantize particles and fields on them. This study is motivated, in part, in order to provide the tools to calculate the rate at which superluminal particles radiate off energy to become infraluminal, as explained above. Remarkably, it is again the three geometric conditions of hyperbolicity, time-orientability and energy-distinguishability that allow the quantization of general linear electrodynamics on an area metric spacetime and the quantization of massive point particles obeying any admissible dispersion relation. We explore the issue of field equations of all possible derivative order in rather systematic fashion, and prove a practically most useful theorem that determines Dirac algebras allowing the reduction of derivative orders. The final part of the thesis presents the sketch of a truly remarkable result that was obtained building on the work of the present thesis. Particularly based on the subtle duality maps between momenta and velocities in general tensorial spacetimes, it could be shown that gravitational dynamics for hyperbolic, time-orientable and energy distinguishable geometries need not be postulated, but the formidable physical problem of their construction can be reduced to a mere mathematical task: the solution of a system of homogeneous linear partial differential equations. This far-reaching physical result on modified gravity theories is a direct, but difficult to derive, outcome of the findings in the present thesis. Throughout the thesis, the abstract theory is illustrated through instructive examples. / Welche Tensorfelder G auf einer glatten Mannigfaltigkeit M können eine Raumzeit-Geometrie beschreiben? Im ersten Teil dieser Dissertation wird es gezeigt, dass nur stark eingeschränkte Klassen von Tensorfeldern eine Raumzeit-Geometrie darstellen können, nämlich Tensorfelder, die eine prädiktive, interpretierbare und quantisierbare Dynamik für Materiefelder ermöglichen. Die offensichtliche Abhängigkeit dieser Charakterisierung erlaubter tensorieller Raumzeiten von einer spezifischen Materiefelder-Dynamik ist keine Schwäche der Theorie, sondern ist letztlich genau das Prinzip, das die üblicherweise betrachteten Lorentzschen Mannigfaltigkeiten auszeichnet: diese stellen die metrische Geometrie dar, welche die Maxwellsche Elektrodynamik prädiktiv, interpretierbar und quantisierbar macht. Materiefeld-Dynamiken, welche die kausale Struktur von Maxwell-Elektrodynamik nicht respektieren, zwingen uns, eine andere Geometrie auszuwählen, auf der die Materiefelder-Dynamik aber immer noch prädiktiv, interpretierbar und quantisierbar sein muss. Diesen drei Voraussetzungen an die Materie entsprechen drei algebraische Voraussetzungen an das total symmetrische kontravariante Tensorfeld P, welches das Prinzipalpolynom der Materiefeldgleichungen (ausgedrückt durch das grundlegende Tensorfeld G) bestimmt: das Tensorfeld P muss hyperbolisch, zeitorientierbar und energie-differenzierend sein. Diese drei notwendigen Bedingungen an die Geometrie genügen, um alle aus der Lorentzschen Geometrie bekannten kinematischen Konstruktionen zu realisieren. Dies zeigen wir im ersten Teil der vorliegenden Arbeit unter Verwendung eines teilweise recht subtilen Wechselspiels zwischen konvexer Analysis, der Theorie partieller Differentialgleichungen und reeller algebraischer Geometrie. Im zweiten Teil dieser Dissertation erforschen wir allgemeine Eigenschaften aller solcher hyperbolischen, zeit-orientierbaren und energie-differenzierenden Geometrien. Physikalisch wichtig sind der Aufbau von frei fallenden und nicht rotierenden Laboratorien, das Auftreten modifizierter Energie-Impuls-Beziehungen und die Identifizierung eines Mechanismus, der erklärt, warum massive Teilchen, die sich schneller als einige masselosse Teilchen bewegen, Energie abstrahlen können, aber nur bis sie sich langsamer als alle masselossen Teilchen bewegen. Im dritten Teil der Dissertation ergründen wir die Quantisierung von Teilchen und Feldern auf tensoriellen Raumzeit-Geometrien, die die obigen physikalischen Bedingungen erfüllen. Eine wichtige Motivation dieser Untersuchung ist es, Techniken zur Berechnung der Zerfallsrate von Teilchen zu berechnen, die sich schneller als langsame masselose Teilchen bewegen. Wir finden, dass es wiederum die drei zuvor im klassischen Kontext identifizierten Voraussetzungen (der Hyperbolizität, Zeit-Orientierbarkeit und Energie-Differenzierbarkeit) sind, welche die Quantisierung allgemeiner linearer Elektrodynamik auf einer flächenmetrischen Raumzeit und die Quantizierung massiver Teilchen, die eine physikalische Energie-Impuls-Beziehung respektieren, erlauben. Wir erkunden auch systematisch, wie man Feldgleichungen aller Ableitungsordnungen generieren kann und beweisen einen Satz, der verallgemeinerte Dirac-Algebren bestimmt und die damit Reduzierung des Ableitungsgrades einer physikalischen Materiefeldgleichung ermöglicht. Der letzte Teil der vorliegenden Schrift skizziert ein bemerkenswertes Ergebnis, das mit den in dieser Dissertation dargestellten Techniken erzielt wurde. Insbesondere aufgrund der hier identifizierten dualen Abbildungen zwischen Teilchenimpulsen und -geschwindigkeiten auf allgemeinen tensoriellen Raumzeiten war es möglich zu zeigen, dass man die Gravitationsdynamik für hyperbolische, zeit-orientierbare und energie-differenzierende Geometrien nicht postulieren muss, sondern dass sich das Problem ihrer Konstruktion auf eine rein mathematische Aufgabe reduziert: die Lösung eines homogenen linearen Differentialgleichungssystems. Dieses weitreichende Ergebnis über modifizierte Gravitationstheorien ist eine direkte (aber schwer herzuleitende) Folgerung der Forschungsergebnisse dieser Dissertation. Die abstrakte Theorie dieser Doktorarbeit wird durch mehrere instruktive Beispiele illustriert.

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Thesis (Ph. D.)--University of Texas at Austin, 2004. / Supervisor: Herbert L. Berk. Vita. Includes bibliographical references.

Orientador: Marcio Jose Menon / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-08-08T18:13:00Z (GMT). No. of bitstreams: 1 Campos_SergioDias_D.pdf: 3049430 bytes, checksum: f2701863943e7b7c98d60318e0719bb2 (MD5) Previous issue date: 2007 / Resumo: Neste trabalho apresentamos um estudo dos processos de espalhamentos elásticos próton-próton ( pp) e antipróton-próton (¯pp) em altas energias analisando, mais especificamente, o comportamento da seção de choque total, da seção de choque diferencial elástica e do parâmetro ñ , que corresponde à razão entre as partes real e imaginária da amplitude de espalhamento elástico frontal. Neste estudo apresentamos uma descrição destas quantidades através de uma parametrização independente de modelo para a amplitude de espalhamento elástico que possui como caráter inovador uma dependência explícita não só com o momento transferido, mas também com a energia da colisão. Este formalismo, além das dependências explícitas, faz uso das relações de dispersão derivativas, possibilitando, via termo de cruzamento entre as amplitudes de espalhamento elástico próton-próton e antipróton-próton, um ajuste conjunto dos dados de seção de choque total, seção de choque diferencial elástica e do parâmetro p para os eventos de colisão pp e ¯pp , simultaneamente. Através desta parametrização, podemos fazer previsões de comportamento para as grandezas citadas anteriormente em energias e momentos transferidos não considerados durante o processo de ajuste (interpolações e extrapolações). Utilizando os parâmetros obtidos através dos ajustes realizados, podemos também fazer previsões para outras grandezas físicas não consideradas na fase de ajustes e neste trabalho, em particular, investigamos o comportamento da inclinação (inclinação da seção de choque diferencial elástica). Além disto, a partir destes parâmetros extraímos o comportamento das seguintes grandezas no espaço de parâmetro de impacto: função de perfil, função eiconal e função de recobrimento inelástica. Apresentamos também uma discussão dos resultados independentes de modelo obtidos neste trabalho nos contextos experimental (experimentos em operação e a serem realizados) e fenomenológico (modelos representativos para interações elásticas pp e ¯pp ) / Abstract: We present a study on proton-proton (pp) and antiproton-proton (¯pp) elastic scattering at high energies, with focus on the behavior of the total cross section, differential cross section and the parameter p (ratio between the real and the imaginary parts of the forward amplitude). These quantities are described by means of a model independent parametrization for the scattering amplitude, with explicit dependence not only on the momentum transfer but also on the collision energy. The formalism makes use of derivative dispersion relations so as to connect real and imaginary parts of the amplitude and, simultaneously, the crossed channels ( and ¯pp ) through analyticity properties. Simultaneous fits to total cross section, differential cross section and p data, from pp and ¯pp scattering, allow a good description of these quantities and also predictions for other quantities (in particular the slope parameter) and at other energies and momentum that did not take part in the fit procedure. From the fit results we extract the behavior of the profile, eikonal and inelastic overlap function as function of the energy and the impact parameter. We also present a discussion on the model independent predictions in the experimental context (running and planned experiments) as well as in the phenomenological context (some representative models for high-energy elastic scattering) / Doutorado / Física das Particulas Elementares e Campos / Doutor em Ciências

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<p>Waves are a fundamental feature in many parts of physics, since they transport energy without transporting matter. This is the case also in space physics. Waves are responsible for energy transport both between different parts of space and between different particles in the space plasma. They are also useful for diagnostics of the space plasma itself. The present thesis considers two different parts of the large subject of space plasma waves: Lower hybrid cavities (LHCs) and simple-pole particle distribution functions.</p><p>The LHCs are localised density depletions that have been observed by several spacecraft. They have increased wave activity in the lower hybrid frequency range, and was previously found on altitudes up to 1750 km. New observations by the Viking and Cluster satellites show that they are common magnetospheric features, at least up to an altitude of 35,000 km. Theoretical results, assuming a cylindrically symmetric density depletion, show that even though the density depletion may decrease slowly with increasing radial distance, and thus be essentially infinite in extent, there is a maximum distance within which a trapped mode, with given wave number <i>k</i><i>z</i> parallel to the geomagnetic field, may propagate. Furthermore, there is a local relation between the plasma density gradient and the lowest possible frequency that the trapped waves can have, for any monotonic density and given <i>k</i><i>z</i>. The combined theoretical and observational results indicate that the length of the cavities is larger than the width by a factor of at least 200.</p><p>Simple-pole particle distribution functions are introduced because they can model high velocity tails of the particle distribution in a way that is not possible to do with Maxwellian distribution functions. These distributions also simplify the calculations. This gives new possibilities for the physical understanding, as well as the numerical calculations, of the dispersion relations of real space plasmas. The dispersion relations of plasmas described by simple-pole distributions are examined, both for unmagnetised and for magnetised plasmas. These examples show how particle populations with the same density and mean particle energy, but with somewhat different distribution functions, have different wave propagation properties that should be observable by existing spacecraft.</p>

Waves are a fundamental feature in many parts of physics, since they transport energy without transporting matter. This is the case also in space physics. Waves are responsible for energy transport both between different parts of space and between different particles in the space plasma. They are also useful for diagnostics of the space plasma itself. The present thesis considers two different parts of the large subject of space plasma waves: Lower hybrid cavities (LHCs) and simple-pole particle distribution functions. The LHCs are localised density depletions that have been observed by several spacecraft. They have increased wave activity in the lower hybrid frequency range, and was previously found on altitudes up to 1750 km. New observations by the Viking and Cluster satellites show that they are common magnetospheric features, at least up to an altitude of 35,000 km. Theoretical results, assuming a cylindrically symmetric density depletion, show that even though the density depletion may decrease slowly with increasing radial distance, and thus be essentially infinite in extent, there is a maximum distance within which a trapped mode, with given wave number kz parallel to the geomagnetic field, may propagate. Furthermore, there is a local relation between the plasma density gradient and the lowest possible frequency that the trapped waves can have, for any monotonic density and given kz. The combined theoretical and observational results indicate that the length of the cavities is larger than the width by a factor of at least 200. Simple-pole particle distribution functions are introduced because they can model high velocity tails of the particle distribution in a way that is not possible to do with Maxwellian distribution functions. These distributions also simplify the calculations. This gives new possibilities for the physical understanding, as well as the numerical calculations, of the dispersion relations of real space plasmas. The dispersion relations of plasmas described by simple-pole distributions are examined, both for unmagnetised and for magnetised plasmas. These examples show how particle populations with the same density and mean particle energy, but with somewhat different distribution functions, have different wave propagation properties that should be observable by existing spacecraft.

Orientador: Marcio Jose Menon / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-12T16:24:49Z (GMT). No. of bitstreams: 1 Avila_ReginaFonseca_D.pdf: 3530629 bytes, checksum: 01dc8228fc148fa58b57ef51867e8ee9 (MD5) Previous issue date: 2009 / Resumo: Apresentamos um estudo amplo e abrangente do espalhamento elástico de há drons em altas energias através de três abordagens distintas: analítica, empírica e fenomenológica. A primeira 'e caracterizada pelos princípios de analiticidade e cruzamento, limites polinomiais para a amplitude de espalhamento e relações de dispersão. Em especial, para classes de funções de interesse físico, introduzimos novas relações de dispersão derivativas, que são equivalentes às relações de dispersão integrais. Na segunda abordagem, decorrente do princípio de Unitaridade, tratamos a Representação Eiconal. Nesse contexto, a partir de uma parametrização empírica para a amplitude de espalhamento e um método analítico-numérico, determinamos a eiconal no espaço de momento transferido, de forma independente de modelo. Em especial, obtemos evidência estatística de que a parte imaginária da eiconal apresenta um zero (troca de sinal); as implicações desse zero no contexto fenomenológico são discutidas em certo detalhe. Na abordagem fenomenológica, através de um modelo baseado no formalismo de Regge, estudamos as contribuições do Odderon (amplitude ímpar) e Pomeron (amplitude par) no regime de altas energias. Em especial, descrevemos novos procedimentos que podem levar à detecção do Odderon nos experimentos a serem realizados com aceleradores de partículas, o "Relativistic Heavy Íon Collider"(RHIC) e "Large Hadron Collider"(LHC). / Abstract: We investigate high-energy elastic hadron scattering by means of three different approaches: analytical, empirical, and phenomenological. The first one is characterized by the fundamental principles of analyticity and crossing symmetry, polynomial limits for the scattering amplitude and dispersion relations. In special, for classes of functions of physical interest, we introduce novel derivative dispersion relations wich are equivalent to integral dispersion relations. In the second approach, based on unitarity principle, we treat the eikonal representation. In this context, by means of an empirical parametrization for the scattering amplitude and an analytical-numerical method, we extract the eikonal in the momentum transfer space, in a model independent way. In special, we obtain statistical evidence that the imaginary part of eikonal presents a zero (change of sign) in the momentum transfer space; the implication of this zero in the phenomenological context is discussed in certain detail. In the third approach, through a model based on the Regge formalism, we investigate the contributions of the Odderon (odd amplitude) and the Pomeron (even amplitude) in the high energy region. In special, we describe new procedures that can lead to the detection of the Odderon in the experiments to be performed in particle accelerators, Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC). / Doutorado / Fisica-Matematica / Doutor em Matemática Aplicada