Die Johannese geskrifte (Evangelie en Briewe) word veralgemenend binne die Christendom gelees en die uniekheidsbeklemtoninge ten opsigte van Jesus as enige Verlosser word ook so verstaan. Hierdie hoofsaaklik sosiaal-wetenskaplike ondersoek was gefokus op Johannes se aansprake ten opsigte van Jesus en is gedoen om bewus te maak van die sosiaal-kulturele onderbou van die geskrifte. As sodanig is dit bedoe! om heuristies in te werk ten einde bestaande hermeneuse beter te dien sodat die boodskap van die Nuwe Testament effektiewer oorgedra kan word. Dit is ook gepoog om bevindinge uit die studie deur te trek na die gesekulariseerde samelewing en pluralistiese religieuse standpunt wat te Iande bestaan. Die teksgedeeltes wat eksegeties ondersoek is, bevat die aspekte van aanvaarding of verwerping van Jesus as die unieke Godsagent wat ewige /ewe meedeel. Dit het geblyk dat die begrip in Johannes nie net op oneindigheid in die hiemamaals dui nie, maar veral op kwaliteit in die hede. Johannes se postulaat is dat Jesus konstant hierdie lewe meedeel aan hulle wat in Hom glo. Die vraag na relevansie van 'n religie uit Judaistiese oorsprong in 'n AfroWesterse samelewing en kultuur is vanuit die aspekte van kulturele relatiwisme en relatiwiteit hanteer. Dit word aanvaar dat die ingrype van God deur Jesus Christus binne die Israelitiese volksmilieu en Mediterreense kultuur plaasgevind het, maar dat dit wat Johannes aan sy lesers herbevestig het, vir aile mense relevant is. Jesus is die unieke Godsagent wat ewige lewe meedeel, wat, as sodanig, nie menslike sterflikheid negeer nie, maar dit transendeer. / The social-scientific research for this treatise concentrated on John's assertion of Jesus' uniqueness. The selected Scripture portions for exegesis contain the aspects of receiving or rejecting Him as God's Agent who bestows eternal life. Eternal lifo in John does not so much denote never ending life, but rather excellent quality of life in the present. The relevancy of a religion from a Judaistic origin in an Afro-Western cultural society was treated on the aspects of cultural relativism and cultural relativity. The conclusion accedes to the fact that God's interaction with man in the person of Jesus Christ took place within an Israelite national milieu and Mediterranean culture, but what John reasserted is relevant for all time- the life that Jesus bestows does not negate mortality, but transcends it. / New Testament / M. Th. (Nuwe Testament)

Submitted by Vasti Diniz (vastijpa@hotmail.com) on 2017-09-12T13:00:44Z No. of bitstreams: 1 arquivototal.pdf: 2334284 bytes, checksum: c3d087bb8f68c3b8f619b05f161a3e77 (MD5) / Made available in DSpace on 2017-09-12T13:00:44Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 2334284 bytes, checksum: c3d087bb8f68c3b8f619b05f161a3e77 (MD5) Previous issue date: 2016-02-25 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / In this thesis, we study the influence of gravitating non-Abelian cosmic strings on the spacetime geomerty. In order to develop this analysis, we constructed a set of coupled non-linear differential equations. Because there is no closed solution for this set of equations, we solve it numerically to determine the behaviour for the Higgs, gauge and metric fields. This model under consideration present two bosonic sectors, besides the non-Abelian gauge field. The two bosonic sectors may present a direct coupling. So, we investigate the relevance of this coupling on the system, specifically in the linear energy density of the string and on the planar angle deficit. We also analyze the behaviors of these quantities as function of the energy scale where the gauge symmetry is spontaneously broken. We have extented this analysis to de Sitter and anti-de Sitter spacetimes. In order to do that we construct the complete set of equations of motion considering the presence of a cosmological constant. By using numerical analysis we provide the behavior of the Higgs and gauge fields and also for the metric tensor for specific values of the physical parameters of the theory. For de Sitter case, we find the appearance of horizons that although being consequence of the presence of the cosmological constant it strongly depends on the value of the gravitational coupling. In the anti-de Sitter case, we find that the system does not present horizons. In fact the new feature of this system is related with the behavior of the (tt) and (zz) components of the metric tensor. They present a strongly increasing for large distance from the string. / Nesta tese estudamos a influência das cordas cósmicas não-Abelianas na geometria do espaço-tempo. Para este fim, utilizamos um modelo de Higgs não-Abeliano acoplado com a gravidade e obtemos um sistema de equações diferenciais não-lineares. Como este sistema de equações diferenciais não possui solução analítica, realizamos análise numérica para obter o comportamento dos campos de Higgs, de gauge e métricos em função da distância à corda cósmica. O modelo considerado apresenta dois campos bosônicos e um campo de gauge não-Abeliano. Como os dois setores bosônicos podem apresentar um acoplamento direto, investigamos a relevância deste acoplamento no sistema, especificamente na densidade linear de energia e no déficit de ângulo planar. Também analisamos o comportamento destas quantidades como função da escala de energia onde a simetria de gauge é espontaneamente quebrada. Ampliamos este estudo para as cordas cósmicas não-Abelianas no espaço-tempo de de Sitter e anti-de Sitter. Para isto, construímos um sistema de equações de campo considerando a presença da constante cosmológica. Utilizando a análise numérica, fornecemos o comportamento dos campos de Higgs, de gauge e dos campos métricos para valores específicos dos parâmetros físicos do modelo. Para o caso do espaço-tempo de de Sitter, salientamos o surgimento do horizonte cosmológico que, embora seja consequência da constante cosmológica, está fortemente relacionado ao acoplamento gravitacional. Para o espaço-tempo de anti-de Sitter, encontramos que o sistema não apresenta horizonte. Esta característica do sistema está relacionada às componentes (tt) e (zz) do tensor métrico, que divergem para grandes distâncias da corda cósmica.

Acompanha: Produto educacional: uma sequência didática para ensinar relatividade restrita no ensino médio com o uso de TIC / FUNPESQ / A Sequência Didática proposta neste trabalho contempla as recomendações dos Parâmetros Curriculares Nacionais (PCN), no sentido de uma progressiva inserção da Física do século XX no ensino médio, tema este que, infelizmente, ainda é muito pouco abordado nas salas de aula do país. O uso das Tecnologias de Informação e Comunicação (TIC) na educação pode proporcionar processos de educação mais participativos, tornando a relação professor‐aluno mais aberta e interativa. Com este intuito, o presente trabalho apresenta a aplicação de uma sequência didática, incluindo suas análises e resultados em sala de aula, para o ensino da Relatividade Restrita aos alunos do ensino médio de um Colégio da rede particular de ensino, no município de Apucarana-Pr. A proposta tem como base teórica a Aprendizagem Significativa de David Ausubel. A sequência em questão faz uso sistemático de recursos computacionais, com destaque para uma planilha original desenvolvida em Excel, com o propósito de melhorar o entendimento de conceitos básicos da Relatividade Restrita, bem como para a dedução de relações matemáticas fundamentais que são decorrência lógica dos postulados de Einstein. Além deste recurso, também foi utilizada a História da Ciência para contextualizar os alunos acerca do momento histórico em que o mundo estava inserido na época que a Teoria da Relatividade Restrita foi desenvolvida. Com isto, os alunos puderam ainda aprender um pouco sobre a vida, a obra e a contribuição deixada por Albert Einstein. Ainda foi utilizado um trecho do filme Interestelar que aborda a viagem no tempo, além de simuladores computacionais. Todos os recursos foram aplicados buscando aproximar a tecnologia (bem conhecida dos jovens) com a sala de aula, com o intuito de melhorar o processo de ensino-aprendizagem. Nossos resultados apontam que a utilização das TIC neste processo propiciam uma aula interativa e dinâmica tanto para o aluno quanto para o professor. Sendo assim, podemos dizer que a proposta aplicada possui um grande potencial pedagógico, pois os alunos, no decorrer da aplicação, mostraram-se mais motivados para as aulas de física. Acreditamos que esse seja o primeiro passo para que a aprendizagem ocorra de forma significativa. / The Didactic sequence proposed in this paper considers the recommendations of the National Curriculum Parameters (PCN), towards a gradual integration of twentiethcentury physics in high school, a topic that unfortunately is still very little explored in the country's classrooms. The use of Information and Communication Technologies (ICT) in education can provide more participatory education process, making it more open and interactive teacher-student relationship. To this end, this work presents the application of a didactic sequence, including its analysis and results in the classroom for teaching relativity to high school students of the College of private schools in the municipality of Apucarana- Pr. The proposal is based on theoretical Meaningful Learning of David Ausubel. The sequence in question is systematic use of computational resources, especially an original spreadsheet developed in Excel, in order to improve understanding of basic concepts of relativity, as well as the deduction of fundamental mathematical relationships that are logical consequence of the postulates Einstein. In addition to this feature, it was also used the History of Science to contextualize students about the historical moment in which the world was inserted at the time that the theory of relativity was developed. With this, students could still learn a little about life, work and contribution left by Albert Einstein. Interstellar a movie part that deals with time travel, and computer simulators also was used. All resources were applied seeking to approach the technology (well-known youth) in the classroom, in order to improve the teachinglearning process. Our results indicate that the use of ICT in this process provide an interactive lesson and dynamic for both the student and the teacher. Thus, we can say that the proposal applied has a great pedagogical potential as students, during the application, were more motivated to physics classes. We believe this is the first step in learning to occur significantly.

Elaboramos um estudo detalhado de alguns aspectos d(e uma versão d)a correspondência AdS/CFT, conjeturada por Maldacena e Witten, entre teorias quânticas de campo num fundo gravitacional dado por um espaço-tempo assintoticamente anti-de Sitter (AAdS), e teorias quânticas de campos conformalmente covariantes no infinito conforme (no sentido de Penrose) deste espaço-tempo, aspectos estes: (a) independentes d(o par d)e modelos específicos em Teoria Quântica de Campos, e (b) suscetíveis a uma reformulação em moldes matematicamente rigorosos. Adotamos como ponto de partida o teorema demonstrado por Rehren no contexto da Física Quântica Local (também conhecida como Teoria Quântica de Campos Algébrica) em espaços-tempos anti-de Sitter (AdS), denominado holografia algébrica ou dualidade de Rehren. O corpo do presente trabalho consiste em estender o resultado de Rehren para uma classe razoavelmente geral de espaços-tempos AAdS d-dimensionais (d>3), escrutinar como as propriedades desta extensão são enfraquecidas e/ou modificadas em relação ao espaço-tempo AdS, e como efeitos gravitacionais não-triviais se manifestam na teoria quântica no infinito conforme. Dentre os resultados obtidos, citamos: condições razoavelmente gerais sobre geodésicas nulas no interior (cuja plausibilidade justificamos por meio de resultados de rigidez geométrica) não só garantem que a nossa generalização é geometricamente consistente com causalidade, como também permite uma reconstrução ``holográfica\'\' da topologia do interior na ausência de horizontes e singularidades; a implementação das simetrias conformes na fronteira, que associamos explicitamente a uma família de isometrias assintóticas do interior construída de maneira intrínseca, ocorre num caráter puramente assintótico e é atingida dinamicamente por um processo de retorno ao equilíbrio, mediante condições de contorno adequadas no infinito; efeitos gravitacionais podem eventualmente causar obstruções à reconstrução da teoria quântica no interior, ou por torná-la trivial em regiões suficientemente pequenas ou devido à existência de múltiplos vácuos inequivalentes, que por sua vez levam à existência de excitações solitônicas localizadas ao redor de paredes de domínio no interior, similares a D-branas. As demonstrações fazem uso extensivo de geometria Lorentziana global. A linguagem empregada para as teorias quânticas relevantes para nossa generalização da dualidade de Rehren segue a formulação funtorial de Brunetti, Fredenhagen e Verch para a Física Quântica Local, estendida posteriormente por Sommer para incorporar condições de contorno. / We elaborate a detailed study of certain aspects of (a version of) the AdS/CFT correspondence, conjectured by Maldacena and Witten, between quantum field theories in a gravitational background given by an asymptotically anti-de Sitter (AAdS) spacetime, and conformally covariant quantum field theories in the latter\'s conformal infinity (in the sense of Penrose), aspects such that: (a) are independent from (the pair of) specific models in Quantum Field Theory, and (b) susceptible to a recast in a mathematically rigorous mould. We adopt as a starting point the theorem demonstrated by Rehren in the context of Local Quantum Physics (also known as Algebraic Quantum Field Theory) in anti-de Sitter (AdS) spacetimes, called algebraic holography or Rehren duality. The main body of the present work consists in extending Rehren\'s result to a reasonably general class of d-dimensional AAdS spacetimes (d>3), scrutinizing how the properties of such an extension are weakened and/or modified as compared to AdS spacetime, and probing how non-trivial gravitational effects manifest themselves in the conformal infinity\'s quantum theory. Among the obtained results, we quote: not only does the imposition of reasonably general conditions on bulk null geodesics (whose plausibility we justify through geometrical rigidity techniques) guarantee that our generalization is geometrically consistent with causality, but it also allows a ``holographic\'\' reconstruction of the bulk topology in the absence of horizons and singularities; the implementation of conformal symmetries in the boundary, which we explicitly associate to an intrinsically constructed family of bulk asymptotic isometries, have a purely asymptotic character and is dynamically attained through a process of return to equilibrium, given suitable boundary conditions at infinity; gravitational effects may cause obstructions to the reconstruction of the bulk quantum theory, either by making the latter trivial in sufficiently small regions or due to the existence of multiple inequivalent vacua, which on their turn lead to the existence of solitonic excitations localized around domain walls, similar to D-branes. The proofs make extensive use of global Lorentzian geometry. The language employed for the quantum theories relevant for our generalization of Rehren duality follows the functorial formulation of Local Quantum Physics due to Brunetti, Fredenhagen and Verch, extended afterwards by Sommer in order to incorporate boundary conditions. (An English translation of the full text can be found at arXiv:0712.0401)

A presente dissertação tem como objeto de estudo sistemas da física da matéria condensada que sejam capazes de simular sistemas gravitacionais, tais como buracos negros e universos em expansão, onde processos quânticos tomam parte. Neste estudo nos debruçamos principalmente sobre o modelo do fluido e condensados de Bose-Einstein. No modelo do fluido exploramos a geometria efetiva que surge e os problemas de back-reaction e dos modos trans-planckianos de campos quânticos. No modelo baseado em condensados exploramos sua faceta cosmológica e a possibilidade de campos maciços. Além destes dois modelos de grande relevância na literatura, ainda expomos os análogos em cordas elásticas e os baseados em ondas na superfícies de fluidos e uma análise geral baseada no formalismo lagrangeano para campos. / This dissertation has as object of study systems of condensate-matter physics which can simulate gravitational systems like black holes and expanding universes where quantum processes take place. In this study we lay attention mainly on the fluid model and on Bose-Einstein-condensate-based models. In the fluid model we explore the features of the emergent geometry and other problems like the back-reaction and the trans-planckian modes of quantum fields. In the condensate-based models we explore their cosmological aspects and the possibility for massive fields. Moreover, we shall present two other models, the elastic string and the surface-wave-based models in fluids, and a very general analysis based on the Lagrangean formalism for fields.

Submitted by isabela.moljf@hotmail.com (isabela.moljf@hotmail.com) on 2017-08-09T11:18:45Z No. of bitstreams: 1 sebastiaomaurofilho.pdf: 637836 bytes, checksum: 0629945b7a9ce79385454dd5fb18c92f (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-08-09T13:36:52Z (GMT) No. of bitstreams: 1 sebastiaomaurofilho.pdf: 637836 bytes, checksum: 0629945b7a9ce79385454dd5fb18c92f (MD5) / Made available in DSpace on 2017-08-09T13:36:52Z (GMT). No. of bitstreams: 1 sebastiaomaurofilho.pdf: 637836 bytes, checksum: 0629945b7a9ce79385454dd5fb18c92f (MD5) Previous issue date: 2017-01-26 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Nesta tese aplicamos o método perturbativo, em nível clássico, à Gravidade de Quarta Ordem e à Relatividade Geral estendida pelo Grupo de Renormalização (RGGR). Para explorar as perturbações métricas, na teoria da Gravidade de Quarta Ordem, nós usamos a formulação de campos auxiliares para uma métrica de fundo curva e arbitrária. O caso em que a métrica de fundo é Ricci-plano foi elaborada em detalhes. Notamos que o uso de campos auxiliares tornará a análise perturbativa mais simples e os resultados mais claros. Como uma aplicação, nós reconsideramos os resultados para a estabilidade do buraco negro de Schwarzschild e discutimos alguns avanços para o buraco negro de Kerr na Gravidade de Quarta Ordem. Nós também usamos o método perturbativo para explorar os limites newtoniano e pós-newtoniano de RGGR. No Sistema Solar, RGGR depende de um único parâmetro adimensional /9, e ele é tal que para /9 = 0 a Relatividade Geral é obtida. Para estudar o limite newtoniano fizemos uso da técnica de transformação conforme e da dinâmica do vetor de Laplace-Runge-Lenz (LRL). Isso nos permitiu estimar o limite superior de P dentro do Sistema Solar em dois casos: um quando é levado em conta o efeito de potencial externo e outro quando ele não é considerado. Anteriormente, foi encontrado que este parâmetro satisfaz o seguinte limite /9 < 10-21, quando o efeito de potencial externo é ignorado. Entretanto, como nós mostramos esse limite cresce cinco ordens de magnitude P < 10-16 quando tal efeito é considerado. Além disso, mostramos que para um certo limite, RGGR pode ser facilmente testada usando o formalismo parametrizado pós-newtoniano (PPN). / In this thesis we applied the perturbative method, on a classical level, to the fourth-order gravity and the Renormalization Group extended General Relativity (RGGR). We will consider auxiliary fields formulation for the general fourth-order gravity on an arbitrary curved back-ground to analyze the metric perturbations in this theory. The case of a Ricci-flat background was elaborated in detail. We noticed that the use of auxiliary fields helps to make the pertur-bative analysis easier and the results more clear. As an application we reconsider the stability problem of the Schwarzschild and Kerr black holes in the fourth-order gravity. We also used the perturbative method to develop the Newtonian and post-Newtonian limits of RGGR. In the Solar System, RGGR depends on a single dimensionless parameter 0, and this parameter is such that for 0 = 0 one fully recovers General Relativity in the Solar System. In order to study the Newtonian limit we used the conformal transformation technique and the dynamics of the Laplace-Runge-Lenz vector (LRL). In this way, we could estimate the upper bound for 0 within the Solar System in two case: the case where the external potential effect is considered and the another when it is not considered. Previously this parameter was constrained to be 0 < 10-21, without considering the external potential effect. However, as we showed, when such an effect is considered this bound increases by five orders of magnitude, O < 10-16. Moreover, we showed that under a certain approximation RGGR can be easily tested using the parametrized post-Newtonian (PPN) formalism.

This thesis consists of three articles investigating the asymptotic behaviour of cosmological spacetimes with symmetries arising in Mathematical General Relativity. In Paper A and B, we consider spacetimes with Bianchi symmetry and where the matter model is that of a perfect fluid. We investigate the behaviour of such spacetimes close to the initial singularity ('Big Bang'). In Paper A, we prove that the Strong Cosmic Censorship conjecture holds in non-exceptional Bianchi class B spacetimes. Using expansion-normalised variables, we further show detailed asymptotic estimates. In Paper B, we prove similar estimates in the case of stiff fluids. In Paper C, we consider T2-symmetric spacetimes satisfying the Einstein equations for a non-linear scalar field. To given initial data, we show global existence and uniqueness of solutions to the corresponding differential equations for all future times. In the special case of a constant potential, a setting which is equivalent to a linear scalar field on a background with a positive cosmological constant, we investigate in detail the asymptotic behaviour towards the future. We prove that the Cosmic No-Hair conjecture holds for solutions satisfying an additional a priori estimate, an estimate which we show to hold in T3-Gowdy symmetry. / Denna avhandling består av tre artiklar som undersöker det asymptotiska beteendet hos kosmologiska rumstider med symmetrier som uppstår i Matematisk Allmän Relativitetsteori. I Artikel A och B studerar vi rumstider med Bianchi symmetri och där materiemodellen är en ideal fluid. Vi undersöker beteendet av sådana rumstider nära ursprungssingulariteten ('Big Bang'). I Artikel A bevisar vi att den Starka Kosmiska Censur-förmodan håller för icke-exceptionella Bianchi klass B-rumstider. Med hjälp av expansions-normaliserade variabler visar vi detaljerade asymptotiska uppskattningar. I Artikel B visar vi liknande uppskattningar för stela fluider. I Artikel C betraktar vi T2-symmetriska rumstider som uppfyller Einsteins ekvationer för ett icke-linjärt skalärfält. För givna begynnelsedata visar vi global existens och entydighet av lösningar till motsvarande differentialekvationer för all framtid. I det speciella fallet med en konstant potential, en situation som motsvarar ett linjärt skalärfält på en bakgrund med en positiv kosmologisk konstant, undersöker vi i detalj det asymptotiska beteendet mot framtiden. Vi visar att den Kosmiska Inget-Hår-förmodan håller för lösningar som uppfyller en ytterligare a priori uppskattning, en uppskattning som vi visar gäller i T3-Gowdy-symmetri. / <p>QC 20171220</p>

Une notion relative (formée d’un concept de base et d’un qualificatif) pourrait apparaître comme unedisposition équivoque. Le principe de légalité impose cependant de fonder toute décision sur unenorme de référence ; la saisine d’une juridiction laisse d’ailleurs supposer que le justiciable en a uneconnaissance spontanée, ni le contexte législatif ni des mesures d’instruction ne suffisant à corrigerl’imprécision linguistique de la loi. Si la coutume permet d’expliciter le concept de base, elle necirconscrit pas pour autant le seuil induit par le qualificatif législatif. La marge d’appréciationprétorienne en découlant ne rend alors la sanction concevable qu’en fonction d’une flagrancefactuelle. Cette dernière conduit à renverser la charge probatoire, en faisant peser sur le défendeurla preuve de la normalité des faits au regard de la norme socialement acceptée. Elle exclut aussi duchamp judiciaire les situations insuffisamment caractérisées, suggérant que le Code civil tolère unepart d’anomalie dans la société et impliquant une personnalisation circonstancielle de la décision. Ensomme, la disproportion des faits est seule sanctionnée et implique une pondération des droits enconflit. Ainsi comprise, la relativité procure au droit quelque souplesse, sans entraîner d’arbitrairejudiciaire : elle permet d’englober des situations marginales dans une même finalité politique. Lerecours aux notions relatives participe donc de l’idée de ne pas réglementer par un droit imposé deplano et révèle le recul de l’ordre public de direction. Le danger réside alors dansl’instrumentalisation de la relativité pour en faire un outil légistique d’exaltation des droits subjectifs. / A relative notion (consisting of a basic concept and a qualifier) could appear as an equivocalprovision. However the principle of legality imposes to base every decision on a reference norm ;referral to a court implies moreover that the person subject to trial has a spontaneous knowledge ofit, neither the legislative context nor investigative measures being sufficient to correct the linguisticimprecision of the law. If custom allows to make explicit the basic concept, it doesn’t for all thatdelimit the threshold inferred by the legislative qualifier. The margin of praetorian appreciationfollowing from it renders then the sanction conceivable only according to factual obviousness. Thelatter leads to reverse the onus of proof by loading the defendant with the proof of the normality ofthe facts with regard to the socially accepted norm. It also excludes from the judicial field theinsufficiently characterized situations, suggesting that the civil code tolerates a share of anomaly insociety and entailing a personalization of the decision for the occasion. In short, only thedisproportion of facts is sanctioned and involves a balancing of the rights in dispute. Understood likethis, relativity gives to the law some flexibility without leading to judicial arbitrary : it affords toinclude marginal situations into a same political finality. The recourse to relative notions is akin to theidea to not regulate by a law imposed ipso jure and reveals the retreat of directional public order. Thedanger lies then in the instrumentalization of relativity in order to make of it a legistics tool pavingthe way for an ill-considered flourishing of one’s rights.

Lors de la focalisation d’un laser femtoseconde ultra-intense [I>10¹⁶W/cm²] sur une cible solide, dès le début de l’impulsion le champ laser est suffisant pour totalement ioniser la surface de la cible. Le reste de l’impulsion est ensuite réfléchi dans la direction spéculaire par le plasma dense ainsi créé : c’est un miroir plasma. Le champ laser ultra-intense peut accélérer les électrons au sein du plasma à des vitesses relativistes. Certains sont éjectés vers le vide et ces miroirs plasmas sont ainsi des sources de faisceaux d’électrons énergétiques. De plus, ils rayonnent dans l’extrême ultra-violet (XUV) à chaque période laser, ce qui se traduit par de la génération d’harmoniques d’ordre élevé de la pulsation laser. L’objectif de cette thèse est de mieux comprendre l’interaction laser-plasma sur miroirs plasmas à l’aide de la caractérisation de ces deux observables physiques qui en sont issues : les faisceaux d’électrons relativistes et les faisceaux d’harmoniques d’ordre élevé. Une première partie traite de la mesure des faisceaux harmoniques. Du fait des conditions physiques extrêmes d’interaction, la détection ne peut se faire qu’à une distance macroscopique de la cible. Ainsi la caractérisation des propriétés angulaires de ces faisceaux (réalisée en fonction des conditions d’interaction au cours de travaux précédents) ne fournit que des informations partielles sur l’interaction en elle-même. La ptychographie, une technique de mesure par diffraction cohérente où une sonde est diffractée par un objet, est ici transposée à la génération d’harmoniques sur miroirs plasmas grâce à la micro-structuration optique du plasma à la surface de la cible. Les champs sources harmoniques sont ainsi reconstruits en amplitude et en phase spatiales directement dans le plan cible. Grâce à ces mesures dans différentes conditions d’interaction, des modèles théoriques analytiques d’interaction en régime non relativiste [I<10¹⁸W/cm²] et relativiste [I>10¹⁸W/cm²] développés précédemment sont validés expérimentalement. Une seconde partie de cette thèse est consacrée à l’étude expérimentale des propriétés angulaires et en énergie des faisceaux d’électrons relativistes issus des miroirs plasmas. Une étude théorique et numérique, permet de prouver que ces mesures sont la première observation claire de l’accélération d’électrons relativistes par laser dans le vide (VLA). Enfin, l’étude simultanée des efficacités de génération des faisceaux d’électrons et d’harmoniques montre une corrélation nette entre les deux processus en régime relativiste. / When focusing an ultra-intense femtosecond laser pulse [I>10¹⁶W/cm²] onto a solid target, this target is ionized at the very beginning of the laser pulse. The resulting dense plasma then reflects the laser in the specular direction: it is a plasma mirror. The ultra-intense laser field can accelerate electrons within the plasma at relativistic speeds. Some are ejected towards the vacuum and these plasma mirrors are therefore sources of relativistic electron beams. Moreover, at each optical cycle they radiate in the form of extreme ultraviolet light, resulting in the generation of high-order harmonics of the laser frequency (HHG). The objective of this PhD is to understand laser-plasma interaction though the characterization of high-order harmonics and relativistic electron beams generated from plasma mirrors. The first part deals with harmonic beam measurement. Due to the extreme physical conditions during the interaction, detection can only be performed at macroscopic distance from target. Thus, the characterization of the harmonic beams’ angular properties (carried out as a function of interaction conditions in previous works) only provides partial information on the interaction itself. A technique of coherent diffraction imaging, named ptychography, which consists of diffracting a probe onto an object, is transposed to HHG on plasma mirrors by optically micro-structuring the plasma on a target surface. Harmonic fields are then reconstructed spatially in amplitude and phase directly in the target plane. Thanks to this measurement in different interaction conditions, previously developed theoretical analytical models in non-relativistic regime [I<10¹⁸W/cm²] and relativistic regime [I>10¹⁸W/cm²] are experimentally validated. The second part of the PhD is dedicated to the experimental characterization of angular and spectral properties of relativistic electron beams. A theoretical and numerical study shows that this constitutes the first clear observation of vacuum laser acceleration (VLA). Finally, a simultaneous study of harmonic and electron signals highlights a strong correlation between both processes in the relativistic regime.

Dans cette thèse je me suis intéressé au caractère relativiste de matériaux topologiques tridimensionnels : les semi-métaux de Weyl et les isolants topologiques. Après une introduction aux états de surfaces et aux matériaux topologiques, je discute leurs propriétés de covariance sous les rotations trigonométriques et hyperboliques. Ces transformations me permettent de traiter les équations du mouvement d'un électron dans un champ magnétique ou à la surface, sous l'influence d'un champ électrique ou d'une inclinaison de la relation de dispersion. En première partie, je l'illustre dans le cas de la réponse magnéto-optique des semi-métaux de Weyl, en présence d'une inclinaison. Ces calculs sont en lien avec ma collaboration avec les expérimentateurs du LNCMI à Grenoble pour la caractérisation de la structure de bande de Cd₃As₂ où l'on montre que ce matériau est un semi-métal de Kane et non un semi-métal de Dirac dans la gamme de potentiels chimiques expérimentalement accessible. L'autre partie de cette thèse porte sur les états de surface des isolants topologiques où l'on montre qu'il existe des états de surface massifs au-delà de l'état de surface chiral. Ces états semblent avoir été observés par des études en ARPES d'échantillons de Bi₂Se₃ et Bi₂Te₃ oxydés et par des mesures de transport sur HgTe déformé. J'ai ainsi eu l'occasion de travailler avec les expérimentateurs du LPA à Paris sur le comportement des états de surface de HgTe sous forts effets de champ. Je termine par une discussion des états à l'interface entre un semi-métal de Weyl et un isolant dans le cas où le gap de ce dernier est suffisamment petit pour observer l'effet d'un champ magnétique et d'une inclinaison de la relation de dispersion sur les états de surface. / During my PhD studies I focused on the relativistic properties of threedimensional topological materials, namely Weyl semimetals and topological insulators. After introducing surface states and topological materials I discuss their covariance in trigonometric and hyperbolic rotations. These transformations help to solve the equations of motion of an electron in a magnetic field or at the surface with an applied electric field or with a tilt in the band dispersion. In a first place, I illustrate these transformations for the magneto-optical response of tilted Weyl semimetals. This work is related to my collaboration with experimentalists at LNCMI, Grenoble for characterizing the band structure of Cd₃As₂ where we show that this material is a Kane semi-metal instead of a Dirac semi-metal in the experimentally accessible range of chemical doping. The other part of this thesis is concerned with the surface states of topological insulators. I show that massive surface states can also exist in addition to the chiral surface state due to band inversion. Such states may have already been observed in ARPES measurement of oxidized Bi₂Se₃ and Bi₂Te₃ and in transport measurement of strained bulk HgTe. I show the work we performed with experimentalists at LPA, Paris on the behavior of HgTe surface states for strong field effects. Finally, I discuss the states at the interface of a Weyl semimetal and a small gap insulator. In this situation, an applied magnetic field or the tilt of the band dispersion can strongly affect the observed surface states.