Geometric description of scattering amplitudes

Die vorliegende Dissertation befasst sich mit einigen der neuesten Entwicklungen im Themengebiet der Streuamplituden in schwach gekoppelten Eichtheorien. Der traditionelle störungstheoretische Zugang, der Feynman-Diagramme verwendet, hat sich durchgesetzt und großen Erfolg erzielt, jedoch er ist zunehmend ungeeignet geworden, um mit der Komplexität der Präzisionsberechnungen umzugehen, die heutzutage benötigt sind. Neue Techniken, die zusammenfassend als on-shell Methoden bezeichnet werden, sind entwickelt worden, um die Nachteile und Engpasse dieses Zugangs zu vermeiden. Sie enthüllten eine inhärente (und manchmal unerwartete) Einfachheit der Streuamplituden, oft in Verbindung zur Symmetrien; daneben, erlaubten sie die Entwicklung eines grundverschiedenen, geometrischen Verständnis von Amplituden, bei dem Grassmann-Mannigfaltigkeiten eine zentrale Rolle spielen. Dieses Programm hat sich sehr gut im Rahmen eines speziellen Modells bewährt, der planaren N = 4 super Yang-Mills Theorie. Im Jahr 2013 ist eine bemerkenswerte Vermutung vorgelegt worden, die besagt, dass jede Amplitude ist insgeheim das Volumen eines verallgemeinerten Polytops, das Amplituhedron heißt. In dieser Doktorarbeit, untersuchen wir, nach einer detaillierten Einführung in die on-shell Methoden, den Amplituhedron-Vorschlag ausführlich auf Baumniveau und wir berichten über mehrere Ergebnisse, die zusammen mit anderen Mitarbeitern erreicht worden sind. Wir führen eine Formel ein, die NMHV-Baumniveau Volumenfunktionen als Integrale über eine duale Grassmann-Mannigfaltigkeit darstellt, und damit Triangulationen des Amplituhedrons vermeidet; dann leiten wir eine i\eps-Vorschrift her, die uns erlaubt, sie als Summe von Residuen eines Grassmannschen Integrals aufzubauen, das im Geiste ähnlich zu dem für Amplituden relevanten ist. Anschließend, angeregt von den Schwierigkeiten bei der Verallgemeinerung unserer Ergebnisse, suchen wir nach einer Realisation der Yangschen Symmetrie im Rahmen des Amplituhedrons. Wir zeigen, dass mit den Volumenfunktionen eng verwandte Objekte wirklich invariant unter den Transformationen des Yangians Y(gl(m + k)) sind und denken über die Implikationen davon nach.This dissertation is concerned with some of the most recent developments in the understanding of gauge theory scattering amplitudes at weak coupling. The traditional perturbative approach in terms of Feynman diagrams is well established and has achieved great triumphs, however it has become increasingly unsuited to handle the complexity of the precision calculations needed nowadays. In looking for new ways to avoid its drawbacks and bottlenecks, new techniques have been developed, collectively going under the name of on-shell methods. Beyond unveiling an inherent (and at times unexpected) simplicity of scattering amplitudes - often in connection to symmetries - they helped the rise of a radically different, geometric understanding of them, in which Grassmannian manifolds play a central role. This program has proven very successful in the context of a special model, planar N = 4 super Yang-Mills theory. In 2013 a striking conjecture was put forward, stating that every amplitude is secretly the volume of a generalised polytope, called the amplituhedron. In this thesis, after providing a broad introduction about on-shell methods, we investigate this proposal at tree-level in detail and report on several new results that were obtained in collaboration with other authors. In particular, we present a closed formula for expressing NMHV tree-level volume functions as integrals over a dual Grassmannian, avoiding triangulations of the amplituhedron; we subsequently derive an i\eps-prescription that allows to alternatively construct them as a sum of residues of a Grassmannian integral, similar in spirit to the one relevant for scattering amplitudes. Motivated by the difficulties in moving to more general tree-level volume functions, we then look for a realisation of Yangian symmetry in the framework of the amplituhedron. We prove that objects closely related to the volume functions are in fact invariant under the Yangian Y(gl(m+ k)) and ponder on the implications of this result

Wave propagation in discontinuous media

Wave propagation in discontinuous media, which is of interest for design analysis of underground structures and geotechnical works in general, is studied in this paper with the scattering matrix method. This method determines the response of a system, i.e. the discontinuous medium, excited by an elastic wave. Both P, SV or SH waves can be applied to the model with any oblique angle of incidence. The scattering matrix is composed of reflection and transmission coefficients of a single joint or a set of parallel joints. The analytical solution is obtained in the frequency domain and allows one to consider multiple wave reflections between joints. Reflected and transmitted waves are calculated for one and more joints in dry or fluid filled conditions. The solutions obtained are compared with analytical and numerical solutions available in the literature or obtained independently by using the Distinct Element Metho

Geometric description of scattering amplitudes

Die vorliegende Dissertation befasst sich mit einigen der neuesten Entwicklungen im Themengebiet der Streuamplituden in schwach gekoppelten Eichtheorien. Der traditionelle störungstheoretische Zugang, der Feynman-Diagramme verwendet, hat sich durchgesetzt und großen Erfolg erzielt, jedoch er ist zunehmend ungeeignet geworden, um mit der Komplexität der Präzisionsberechnungen umzugehen, die heutzutage benötigt sind. Neue Techniken, die zusammenfassend als on-shell Methoden bezeichnet werden, sind entwickelt worden, um die Nachteile und Engpasse dieses Zugangs zu vermeiden. Sie enthüllten eine inhärente (und manchmal unerwartete) Einfachheit der Streuamplituden, oft in Verbindung zur Symmetrien; daneben, erlaubten sie die Entwicklung eines grundverschiedenen, geometrischen Verständnis von Amplituden, bei dem Grassmann-Mannigfaltigkeiten eine zentrale Rolle spielen. Dieses Programm hat sich sehr gut im Rahmen eines speziellen Modells bewährt, der planaren N = 4 super Yang-Mills Theorie. Im Jahr 2013 ist eine bemerkenswerte Vermutung vorgelegt worden, die besagt, dass jede Amplitude ist insgeheim das Volumen eines verallgemeinerten Polytops, das Amplituhedron heißt. In dieser Doktorarbeit, untersuchen wir, nach einer detaillierten Einführung in die on-shell Methoden, den Amplituhedron-Vorschlag ausführlich auf Baumniveau und wir berichten über mehrere Ergebnisse, die zusammen mit anderen Mitarbeitern erreicht worden sind. Wir führen eine Formel ein, die NMHV-Baumniveau Volumenfunktionen als Integrale über eine duale Grassmann-Mannigfaltigkeit darstellt, und damit Triangulationen des Amplituhedrons vermeidet; dann leiten wir eine i\eps-Vorschrift her, die uns erlaubt, sie als Summe von Residuen eines Grassmannschen Integrals aufzubauen, das im Geiste ähnlich zu dem für Amplituden relevanten ist. Anschließend, angeregt von den Schwierigkeiten bei der Verallgemeinerung unserer Ergebnisse, suchen wir nach einer Realisation der Yangschen Symmetrie im Rahmen des Amplituhedrons. Wir zeigen, dass mit den Volumenfunktionen eng verwandte Objekte wirklich invariant unter den Transformationen des Yangians Y(gl(m + k)) sind und denken über die Implikationen davon nach.This dissertation is concerned with some of the most recent developments in the understanding of gauge theory scattering amplitudes at weak coupling. The traditional perturbative approach in terms of Feynman diagrams is well established and has achieved great triumphs, however it has become increasingly unsuited to handle the complexity of the precision calculations needed nowadays. In looking for new ways to avoid its drawbacks and bottlenecks, new techniques have been developed, collectively going under the name of on-shell methods. Beyond unveiling an inherent (and at times unexpected) simplicity of scattering amplitudes - often in connection to symmetries - they helped the rise of a radically different, geometric understanding of them, in which Grassmannian manifolds play a central role. This program has proven very successful in the context of a special model, planar N = 4 super Yang-Mills theory. In 2013 a striking conjecture was put forward, stating that every amplitude is secretly the volume of a generalised polytope, called the amplituhedron. In this thesis, after providing a broad introduction about on-shell methods, we investigate this proposal at tree-level in detail and report on several new results that were obtained in collaboration with other authors. In particular, we present a closed formula for expressing NMHV tree-level volume functions as integrals over a dual Grassmannian, avoiding triangulations of the amplituhedron; we subsequently derive an i\eps-prescription that allows to alternatively construct them as a sum of residues of a Grassmannian integral, similar in spirit to the one relevant for scattering amplitudes. Motivated by the difficulties in moving to more general tree-level volume functions, we then look for a realisation of Yangian symmetry in the framework of the amplituhedron. We prove that objects closely related to the volume functions are in fact invariant under the Yangian Y(gl(m+ k)) and ponder on the implications of this result

Yangian Symmetry for the Tree Amplituhedron

17 pages, 4 figures; v2: extended discussion of results, minor typos corrected, version published in Journal of Physics ATree-level scattering amplitudes in planar N=4 super Yang-Mills are known to be Yangian-invariant. It has been shown that integrability allows to obtain a general, explicit method to find such invariants. The uplifting of this result to the amplituhedron construction has been an important open problem. In this paper, with the help of methods proper to integrable theories, we successfully fill this gap and clarify the meaning of Yangian invariance for the tree-level amplituhedron. In particular, we construct amplituhedron volume forms from an underlying spin chain. As a by-product of this construction, we also propose a novel on-shell diagrammatics for the amplituhedron.Peer reviewe

Piperidine Azasugars Bearing Lipophilic Chains: Stereoselective Synthesis and Biological Activity as Inhibitors of Glucocerebrosidase (GCase)

We report a straightforward synthetic strategy for the preparation of trihydroxypiperidine azasugars decorated with lipophilic chains at both the nitrogen and the adjacent carbon as potential inhibitors of the lysosomal enzyme glucocerebrosidase (GCase), which is involved in Gaucher disease. The procedure relies on the preparation of C-erythrosyl N-alkylated nitrones 10 through reaction of aldehyde 8 and primary amines 13 followed by oxidation of the imines formed in situ with the methyltrioxorhenium catalyst and urea hydrogen peroxide. The addition of octylMgBr to nitrone 10e provided access to both epimeric hydroxylamines 21 and 22 with opposite configuration at the newly created stereocenter in a stereodivergent and completely stereoselective way, depending on the absence or presence of BF3·Et2O. Final reductive amination and acetonide deprotection provided compounds 14 and 15 from low-cost d-mannose in remarkable 43 and 32% overall yields, respectively, over eight steps. The C-2 R-configured bis-alkylated trihydroxypiperidine 15 was the best ligand for GCase (IC50 = 15 μM), in agreement with MD simulations that allowed us to identify the chair conformation corresponding to the best binding affinity.MINECO (CTQ2016- 77270-R) and (PID2019-104090RB-100

Towards the Amplituhedron Volume

21 pages; v2: version published in JHEPIt has been recently conjectured that scattering amplitudes in planar N=4 super Yang-Mills are given by the volume of the (dual) amplituhedron. In this paper we show some interesting connections between the tree-level amplituhedron and a special class of differential equations. In particular we demonstrate how the amplituhedron volume for NMHV amplitudes is determined by these differential equations. The new formulation allows for a straightforward geometric description, without any reference to triangulations. Finally we discuss possible implications for volumes related to generic N^kMHV amplitudes.Peer reviewe

Enseñanza basada en el aprendizaje cooperativo mediado por tecnologías educativas en el bachillerato técnico módulo emprendimiento-gestión

The study focuses on cooperative learning mediated by educational technologies in the Entrepreneurship and Management module of the Baccalaureate, with the aim of improving the quality of the teaching-learning process by exploring innovative pedagogical strategies. It is based on the importance of cooperative work in all curricular areas, as well as the need to guarantee the internal coherence of the didactic proposal. It is based on the theory of constructivism and socioconstructivism, which support the idea that students learn best when they actively interact with their environment and build knowledge together. The implementation of this methodology was carried out through carefully designed and administered surveys to a group of intentionally selected students; fundamental ethical practices were followed throughout the research process. Statistical software was used for data analysis, which included specific tests to determine the association between categorical variables and descriptive analysis techniques. These findings support the effectiveness of cooperative learning mediated by educational technologies in the Technical Baccalaureate of the Entrepreneurship and Management module as an innovative pedagogical strategy that promotes collaboration, equal opportunities, the development of social skills and student autonomy. Furthermore, this methodology is aligned with the legal bases of education in Ecuador and is based on various theoretical bases that support its effectiveness.El estudio se centra en el aprendizaje cooperativo mediado por tecnologías educativas en el módulo de Emprendimiento y Gestión del Bachillerato, con el objetivo de mejorar la calidad del proceso de enseñanza-aprendizaje mediante la exploración de estrategias pedagógicas innovadoras. Se basa en la importancia del trabajo cooperativo en todas las áreas curriculares, así como en la necesidad de garantizar la coherencia interna de la propuesta didáctica. Se fundamenta en la teoría del constructivismo y del socioconstructivismo, que apoyan la idea de que los estudiantes aprenden mejor cuando interactúan activamente con su entorno y construyen conocimiento de manera conjunta. La implementación de esta metodología se realizó a través de encuestas cuidadosamente diseñadas y administradas a un grupo de estudiantes seleccionados intencionalmente, se siguieron prácticas éticas fundamentales en todo el proceso de investigación. Se empleó software estadístico para el análisis de datos, que incluyó pruebas específicas para determinar la asociación entre variables categóricas y técnicas de análisis descriptivo. Estos hallazgos respaldan la efectividad del aprendizaje cooperativo mediado por tecnologías educativas en el Bachillerato Técnico del módulo de Emprendimiento y Gestión como una estrategia pedagógica innovadora que promueve la colaboración, la igualdad de oportunidades, el desarrollo de habilidades sociales y la autonomía del estudiante. Además, esta metodología se alinea con las bases legales de la educación en Ecuador y se sustenta en diversas bases teóricas que respaldan su eficacia

Effect of the UAV orientation in antenna pattern measurements

A novel radiation pattern measurement system for VHF and UHF antennas has been recently developed using the Unmanned Aerial Vehicle (UAV) technology. This paper discusses the effect of the UAV orientation and the applicable corrections on the pattern extraction procedure, in order to increase the accuracy and repeatability of the measurements

RENEB accident simulation exercise

Purpose: The RENEB accident exercise was carried out in order to train the RENEB participants in coordinating and managing potentially large data sets that would be generated in case of a major radiological event. Materials and methods: Each participant was offered the possibility to activate the network by sending an alerting email about a simulated radiation emergency. The same participant had to collect, compile and report capacity, triage categorization and exposure scenario results obtained from all other participants. The exercise was performed over 27 weeks and involved the network consisting of 28 institutes: 21 RENEB members, four candidates and three non-RENEB partners. Results: The duration of a single exercise never exceeded 10 days, while the response from the assisting laboratories never came later than within half a day. During each week of the exercise, around 4500 samples were reported by all service laboratories (SL) to be examined and 54 scenarios were coherently estimated by all laboratories (the standard deviation from the mean of all SL answers for a given scenario category and a set of data was not larger than 3 patient codes). Conclusions: Each participant received training in both the role of a reference laboratory (activating the network) and of a service laboratory (responding to an activation request). The procedures in the case of radiological event were successfully established and tested