Das Standardmodell der Teilchenphysik hat sich bis heute, mit Ausnahme der allgemeinen Relativitätstheorie, als erfolgreichste Theorie zur Beschreibung der Natur erwiesen. Störungstheoretische Rechnungen für bestimmte Mengen in Quantenchromodynamik (QCD) haben bisher unerreicht präzise Vorraussagen ermöglicht, die experimentell nachgewiesen wurden. Trotz dieser Erfolge gibt es Teile des Standardmodells und Energieskalen bei denen die Störungstheorie versagt und man nach Alternativen suchen muss. Vieles können wir hierbei verstehen, indem wir eine ähnliche Theorie untersuchen, die sogenannte planare N=4 Super Yang-Millstheorie in vier Dimensionen (N=4 SYM). Es existieren viele Indizien dafür, dass die Theorie exakte Lösungen zulässt. Dies lässt sich zurückführen auf die Integrabilität der Theorie, eine unendlich dimensionale Symmetriealgebra, die die Theorie stark einschränkt. Neben besagter Integrabilität besitzt diese Theorie auch andere spezielle Eigenschaften. So ist sie des am besten verstandenen Beispiels der Eich-/Gravitations Dualität durch die AdS/CFT Korrespondenz. Ausserdem sind die Streuamplituden von Gluonen auf Baumgraphenniveau in N=4 SYM die selben wie in Quantenchromodynamik. Diese Streuamplituden besitzen eine elegante Struktur und stellen sich als deutlich simpler heraus, als die dazugehörigen Feynmangraphen vermuten lassen. Tatsächlich umgehen viele der zur Berechnung von Streuamplituden entwickelten Masseschalenmethoden die Feynmangraphen, indem sie vorrübergehend manifeste Unitarität und Lokalität aufgeben und dadurch die Rechnungen stark vereinfachen. Alle diese Entwicklungen suggerieren, dass der konventionelle Formalismus der Theorie mit Hilfe der Wirkung im Minkowskiraum nicht der aufschlussreichste oder effizienteste Weg ist, die Theorie zu untersuchen. Diese Arbeit untersucht der Hypothese, ob dass stattdessen Twistorvariablen besser geeignet sind, die Theorie zu beschreiben. Der Twistorformalismus wurde zuerst von Roger Penrose eingeführt. Auf dem klassischen Level ist die holomorphe Chern-Simonstheorie im Twistorraum äquivalent zur klassischen selbst-dualen Yang-Mills Lösung in der Raumzeit. Die volle Twistorwirkung, welche eine Störung um diesen klassisch integrablen Sektor ist und durch eine Eichbedingung auf die N=4 SYM Wirkung reduziert werden kann, produziert unter einer anderen Eichbedingung alle sogenannten maximalhelizitätsverletzenden (MHV) Amplituden auf Baumgraphenniveau. Durch die Einführung eines Twistorpropagators konnten auch NkMHV Amplituden effizient beschrieben werden. In dieser Arbeit erweitern wir den Twistorformalismus um auch Größen, die sich nicht auf den Masseschalen befinden, beschreiben zu können. Wir untersuchen alle lokalen eichinvarianten zusammengesetzten Operatoren im Twistorraum und zeigen, dass sie alle Baumgraphenniveau-Formfaktoren des sogenannten MHV-Typs erzeugen. Wir erweitern diese Methode zu NMHV und öher NkMHW Level in Anlehnung an die Amplituden. Schliess lich knüpfen wir an die Integrabilität an, indem wir den ein-Schleifen Dilatationsoperator in dem skalaren Sektor der Theorie im Twistorraum berechnen. / The Standard Model of particle physics has proven to be, with the exception of general relativity, the most accurate description of nature to this day. Perturbative calculations for certain quantities in Quantum Chromo Dynamics (QCD) have led to the highest precision predictions that have been experimentally verified. However, for certain sectors and energy regimes, perturbation theory breaks down and one must look for alternative methods. Much can be learned from studying a close cousin of the standard model, called planar N = 4 super Yang-Mills theory in four dimensions (N = 4 SYM), for which a lot of evidence exists that it admits exact solutions. This exact solvability is due to its quantum integrability, a hidden infinite symmetry algebra that greatly constrains the theory, which has led to a lot of progress in solving the spectral problem. Integrability aside, this non-Abelian quantum field theory is special in yet other ways. For example, it is the most well understood example of a gauge/gravity duality via the AdS/CFT correspondence. Furthermore, at tree level the scattering amplitudes in its gluon sector coincide with those of Quantum Chromo Dynamics. These scattering amplitudes exhibit a very elegant structure and are much simpler than the corresponding Feynman diagram calculation would suggest. Indeed, many on-shell methods that have been developed for computing these scattering amplitudes circumvent the tedious Feynman calculation, by giving up manifest unitarity and locality at intermediate stages of the calculation, greatly simplifying the work. All these developments suggest that the conventional way in which the theory is presented, i.e. in terms of the well- known action on Minkowski space, might not be the most revealing or in any case not the most efficient way. This thesis investigates whether instead twistor variables provide a more suitable description. The twistor formalism was first introduced by Roger Penrose. At the classical level, a holomorphic Chern-Simons theory on twistor space is equivalent to classically integrable self-dual Yang-Mills solutions in space-time. A quantum perturbation around this classically integrable sector reduces to the conventional N = 4 SYM action by imposing a partial gauge condition. This action generates all so-called maximally helicity violating (MHV) amplitudes at tree level directly, when a different gauge was chosen. By including a twistor propagator into the formalism, also higher degree NkMHV amplitudes can be described efficiently. In this thesis we extend this twistor formalism to encompass (partially) off-shell quantities. We describe all gauge-invariant local composite operators in twistor space and show that they immediately generate all tree-level form factors of the MHV type. We use the formalism to compute form factors at NMHV and higher NkMHV level in parallel to how this was done for amplitudes. Finally, we move on to integrability by computing the one-loop dilatation operator in the scalar sector of the theory in twistor space.

Cardiovascular complications associated with elevated levels of glucose in the blood (Hyperglycemia, HG) is a growing health concern. HG is known to be associated with a variety of cardiovascular morbidities including higher incidence of electrical disturbances. Although effects of chronic HG have been widely investigated, electrophysiological effects of acute hyperglycemia are relatively less known. Further, hyperglycemic effects on adrenergic response is not widely investigated. We used excised ventricular tissues from mice to record trans-membrane potentials during a variety of pacing protocols to investigate cellular/tissue level electrophysiological effects of acute hyperglycemia and adrenergic stimulation (1µM Isoproterenol, a β-adrenergic agonist). A custom program was used to compute action potential durations (APD), maximal rates of depolarization (dv/dtmax), and action potential amplitudes (APA) from the recorded trans-membrane potentials. From these computed measures, electrical restitution and alternans threshold were quantified. Restitution was quantified using the Standard Protocol (SP; basic cycle length BCL= 200ms), Dynamic Protocol (DP; 200-40ms or until blockade) and a novel diastolic interval (DI) control protocol with Sinusoidal Changes in DI. Results from 6 mice show that acute hyperglycemia causes prolongation of the APD. Effects of adrenergic stimulation during acute hyperglycemia were partially blunted compared with non-hyperglycemic state, i.e. hyperglycemia minimized the decrease in APD that was produced by adrenergic stimulation. Similar, but less consistent (across animals) effects were seen in other electrophysiological parameters such as alternans threshold. These results show that acute hyperglycemia may itself alter cellular level electrophysiology of myocytes and importantly, modify adrenergic response. These results suggest that in addition to long term re-modeling that occurs in diabetes, acute changes in glucose levels also affect electrical function and further may contribute to systemically observed changes in diabetes by blunting adrenergic response. Therefore, further investigation into the electrophysiological effects of acute changes in glucose levels are warranted.

Nous étudions la force de Casimir entre deux miroirs métalliques à température non nulle. Nous développons les outils théoriques nécessaires à une évaluation précise de cette force et qui permettent une comparaison de haute précision avec les mesures expérimentales récentes. A partir de la notion de réseau optique, nous caractérisons la diffusion des fluctuations du vide électromagnétique sur une cavité Fabry-Perot et calculons la force de Casimir comme la différence des pressions de radiation exercées par ces fluctuations à l'intérieur et à l'extérieur de la cavité. L'effet de réflexion imparfaite des miroirs est pris en compte en étudiant leur réponse optique, d'abord pour des miroirs diélectriques puis pour des miroirs métalliques. Nous détaillons le rôle des propriétés de causalité, de stabilité et de transparence à haute fréquence des amplitudes de diffusion. Nous calculons également la force de Casimir à température ambiante en évaluant l'effet induit par les fluctuations thermiques du champ. En tenant compte simultanément de cet effet et de l'effet de réflexion imparfaite des miroirs, nous montrons que ces deux effets sont corrélés et que cette corrélation doit être considérée pour une évaluation de haute précision. Dans le cadre de notre formulation, nous résolvons la polémique liée au calcul de la force entre miroirs dissipatifs à température non nulle. Finalement, nous analysons les problèmes de géométrie et de rugosité liés aux expériences. En particulier pour la question de la rugosité de surface des miroirs, nous montrons pour des miroirs parfaits que l'approximation de proximité n'est pas toujours valable. Nous insistons sur les effets de sensibilité liés à la dépendance spectrale de la rugosité.

Dans cette thèse on discute l'influence des plasmons de surfaces sur l'effet Casimir entre deux miroirs métalliques plans et parallèles placés à une distance arbitraire. En utilisant le model plasma pour décrire la réponse optique du métal, on exprime l'énergie de Casimir comme une somme des contributions associées aux modes évanescents relatifs aux plasmons de surface et aux modes propagatifs de la cavité. Contrairement à une ce qu'on pouvait attendre, la contribution des modes plasmoniques est essentielle à toute distance afin d'assurer le correct résultat pour l'énergie de Casimir. Un des deux modes plasmoniques génère une contribution répulsive qui compense la contribution attractive provenant des modes propagatifs de la cavité, alors que les deux contributions, prises séparément, sont beaucoup plus importantes que la valeur réelle pour l'énergie de Casimir. Cela suggère qu'il est possible d'ajuster le signe de la force de Casimir en manipulant les plasmons de surface.

Cette thèse décrit quelques développements dans les techniques de calcul des amplitudes de diffusion en théorie supersymétrique de champ de jauge . L'accent est mis sur les relations de récurrence on-shell et sur l'utilisation de méthodes d'unitarité pour des calculs de boucle. En particulier, la récurrence on-shell est liée aux règles BCFW pour calculer les amplitudes de jauge au niveau des arbres. Les combinaisons de techniques de coupe d'unitarité et la récurrence sont utilisées pour calculer les amplitudes de boucle, et finalement, à partir des amplitudes, pour obtenir la fonction de corrélation énergie-énergie en théorie de super-Yang-Mills N = 4 à l'aide de la représentation de Mellin-Barnes. Dans le dernier chapitre, nous tentons de trouver un contour convergent pour les intégrales de Mellin Barnes en multi-dimension obtenu par une certaine approximation d'un contour de phase stationnaire.

Thesis (Ph.D.); Submitted to the Massachusetts Inst. of Tech., Cambridge, MA (US); 1 Oct 2003. / Published through the Information Bridge: DOE Scientific and Technical Information. "JLAB-PHY-03-174" "DOE/ER/40150-2571" Zhengwei Chai. 10/01/2003. Report is also available in paper and microfiche from NTIS.

[pt] Uma das principais etapas na exploração de petróleo é a definição de um modelo geológico que justifique a existência de uma acumulação de hidrocarbonetos. Ferramentas que possam aumentar o grau de precisão deste modelo são foco de constante estudo na indústria do petróleo. Neste contexto, recentemente, Partyka et al. apresentaram uma nova técnica que utiliza a decomposição espectral dos dados sísmicos para refinar o modelo geológico em termos de definição de espessura de camadas. Nesta pesquisa, essa técnica é estudada e testada, e é proposta a utilização da transformada S, desenvolvida por Stockwell et al., para localizar as componentes de freqüência no domínio do tempo. Os testes realizados com dados sintéticos apontam o uso da técnica de Partyka et al. para fins mais qualitativos, já que, quando os modelos dos testes são perturbados, as análises quantitativas ficam comprometidas. A transformada S mostrou bons resultados na localização das componentes de freqüência no domínio do tempo; no entanto, ela acarreta a suavização do espectro de amplitudes. Ao final deste trabalho é apresentado um exemplo da utilização da técnica em dados reais tridimensionais. / [en] One of the main steps in oil exploration is the definition of a geological model that can justify the existence of a hydrocarbon accumulation. Tools that can improve the precision of this geological model are a constant goal of the oil industry research. In this context, Partyka et al. have recently presented a new technique that uses spectral seismic data decomposition in order to improve the model's accuracy in terms of the thickness definition of geological layers. In the present research, this technique is studied and tested, and a use for the S transform is proposed to locate the frequency components in the time domain. The S transform was recently developed by Stockwell et al. The tests performed with synthetic data indicate that the technique developed by Partyka et al. provide a better qualitative response, because, when the models in the tests are disturbed, qualitative analyses are compromised. The S transform showed good results in locating the frequency components in the time domain, but it smoothes the amplitude spectrum. At the end of this work, an example of the use of this technique with real three-dimensional data is presented.

Conformal Field Theories (CFT) are Quantum Field Theories characterized by enhanced (conformal) symmetries. They are interesting to Theoretical Physicists because they occur at critical points in phase transitions of various systems and also in the world sheet formulation of String Theory. CFTs allow Operator Product Expansion (OPE) in their correlators. The idea of Conformal Bootstrap is to solely use the conformal symmetries and crossing symmetry in the OPE to solve a conformal led theory and not explicitly use a lagrangian. Solving a CFT is equivalent to obtaining the anomalous dimensions and OPE coe client’s of the operators. The work presented in this thesis shows how ideas of bootstrap can be used to get analytic results for dimensions and OPE coe client’s of various operators in CFTs. In the conventional bootstrap program, the OPE in the direct (s-) channel is compared with the OPE of a crossed (t-) channel. This requirement of crossing symmetry is called the bootstrap equation. The flow of logic is somewhat reversed in the \new" idea that is formulated in this thesis. The trick is to expand a CFT correlator in terms of Witten diagrams, in all channels. This is a manifestly crossing symmetric description, and is in contrast to the usual expansion in terms of conformal blocks, which is in only one channel. For convenience we work with the Mellin transforms of Witten diagrams. For consistency of the Witten diagrams expansion with the conformal block expansion in a certain channel, we require the satisfaction of some equations, which we call the bootstrap equations in Mellin space. This scheme was rest chalked out by Polyakov in 1973, where he proposed the use of \unitary amplitudes" to expand a correlator. The unitary amplitudes had similar symmetry and analytic properties as the Witten diagrams. Even though he did not take his idea forward, replacing unitary amplitudes with Witten diagrams seems to work very well for obtaining analytic results. The working of bootstrap equations in Mellin space is demonstrated for the 4 Wilson-Fisher fixed point in d = 4 , O(N) theory at Wilson-Fisher point (in d = 4 ), as well as with large N (in general d), and large spin operators in strongly coupled and weakly coupled theories. For the case of global symmetry we have also analysed the somewhat unexplored case of cubic anisotropy. The results are obtained as perturbative series in , 1=N, or 1=` as applicable, and they are consistent with known results in literature. We also obtain various new results, for instance the OPE coe client’s of general higher spin operators. These results are otherwise very di cult to end from Feynman diagrams, but in this approach they come out very simply, essentially by solving some algebraic equations. We also show the use of the conventional bootstrap strategy, for analytically obtaining anomalous dimensions of large spin operators having higher twists, in a O(N) theory, by working in the light cone limit. One can question the validity of the proposal of using Witten diagrams to expand a correlator. One such issue is convergence of the sum over Witten diagrams. Convergence can be shown to hold for the operator spectrum we have worked with. Also there are operators that might upset convergence under some conditions. Resolutions of such cases, and ways to improve convergence have also been discussed. The conventional bootstrap method has been very successful in giving numerical results in nonpertur-bative CFTs, like the 3 dimensional Ising model. Numerical analysis can also be made possible with the new bootstrap in Mellin space approach. Having a convergent basis of expansion improves the prospect of numeric. The goal is to formulate a bootstrap scheme that, under a single framework, can make most of all the CFT properties. It should be systematic, so that one can obtain anomalous dimensions and OPE coe client’s of all operators up to any desired order, and works for all strongly/weakly coupled and perturbative/nonpertur-bative CFTS, both analytically and numerically. Finally, the use of Witten diagrams also indicates the possibility of Ising CFT or weakly coupled CFTs having connections with AdS/CFT, and hence String Theory. It does seem we have a right direction towards achieving our goal.

We begin by studying field-theory amplitude relations such as the Kleiss-Kuijf, Bern-Carrasco-Johansson, Kawai-Lewellen-Tye and the double copy construction, which are important ingredients in this thesis. Going beyond the field-theory limit we study how the gauge-sector of the heterotic string relates to type I amplitudes through the single valued projection of multiple zeta values. At low energy and for a U(1) gauge group (a single brane) the type I amplitudes are generated by the Born-Infeld action, whereas the corresponding heterotic amplitudes vanish in this limit. As a simple exercise we study Yang-Mills theory deformed by a $F^4$ operator, which is the first correction induced by the Born-Infeld action. This exercise is then generalized by considering the four- and six-point amplitudes in Tseytlin's proposal for a non-Abelian Born-Infeld action. Comparing these amplitudes with those found in type I and heterotic string theory we attempt to gain more insight about the non-Abelian Born-Infeld action.

In den vergangenen Jahrzehnten rückte das häufige Auftreten von multiplen Polylogarithmen und multiplen Zeta-Werten, in Feynman-Diagramm Rechnungen niedriger Ordnung, verstärkt in den wissenschaftlichen Fokus. Hierbei offenbarte sich eine Verbindung zu den mathematischen Theorien der Perioden und der iterierten Integrale von Chen. Eine ähnliche Allgegenwärtigkeit von multiplen Zeta-Werten wurde jüngst auch in der α'-Entwicklung von Genus-Null Stringtheorie Amplituden beobachtet. Davon inspiriert befasst sich diese Arbeit mit der Systematik der iterierten Integralen in den Streuamplituden der offenen Stringtheorie. Unser Fokus liegt insbesondere auf der Genus-Eins Amplitude, welche sich vollständig durch iterierte Integrale, die bezüglich einer punktierten elliptischen Kurve definiert sind, ausdrücken lässt. Wir führen den Begriff der getwisteten elliptischen multiplen Zeta-Werte ein. Dieser Begriff beschreibt eine Klasse von iterierten Integralen, die auf einer elliptischen Kurve definiert sind, bei welcher ein rationales Gitter entfernt wurde. Anschließend zeigen wir, dass die Entwicklung eines jeden getwisteten elliptischen multiplen Zeta-Wertes, bezüglich des modularen Parameters τ, durch ein Anfangswertproblem beschrieben wird. Weiterhin präsentieren wir ein Argument dafür, dass sich im Limes τ→i∞ jeder getwistete elliptische multiple Zeta-Wert durch zyklotomische multiple Zeta-Werte ausdrücken lässt. Schließlich beschreiben wir wie sich Genus-Eins Amplituden in offener Stringtheorie mithilfe von getwisteten elliptischen multiplen Zeta-Werten ausdrücken lassen und illustrieren dies für die Vier-Punkt Amplitude. Hierbei zeigt es sich, dass bis zu dritter Ordnung in α' alle Beiträge durch die Unterklasse der elliptischen multiplen Zeta-Werte ausgedrückt werden können, was wiederum äquivalent zu der Abwesenheit unphysikalischer Pole in Gliozzi-Scherk-Olive projizierter Superstringtheorie ist. / Over the last few decades the prevalence of multiple polylogarithms and multiple zeta values in low order Feynman diagram computations of quantum field theory has received increased attention, revealing a link to the mathematical theories of Chen’s iterated integrals and periods. More recently, a similar ubiquity of multiple zeta values was observed in the α'-expansion of genus-zero string theory amplitudes. Inspired by these developments, this work is concerned with the systematic appearance of iterated integrals in scattering amplitudes of open superstring theory. In particular, the focus will be on studying the genus-one amplitude, which requires the notion of iterated integrals defined on punctured elliptic curves. We introduce the notion of twisted elliptic multiple zeta values that are defined as a class of iterated integrals naturally associated to an elliptic curve with a rational lattice removed. Subsequently, we establish an initial value problem that determines the expansions of twisted elliptic multiple zeta values in terms of the modular parameter τ of the elliptic curve. Any twisted elliptic multiple zeta value degenerates to cyclotomic multiple zeta values at the cusp τ → i∞, with the corresponding limit serving as the initial condition of the initial value problem. Finally, we describe how to express genus-one open-string amplitudes in terms of twisted elliptic multiple zeta values and study the four-point genus-one open-string amplitude as an example. For this example we find that up to third order in α' all possible contributions in fact belong to the subclass formed by elliptic multiple zeta values, which is equivalent to the absence of unphysical poles in Gliozzi-Scherk-Olive projected superstring theory.