Cette thèse traite, dans une perspective philosophique, de l'intérêt éthique du dialogue pour l’éducation morale, en utilisant plus spécifiquement comme cadre théorique l’éthique de la sollicitude de Nel Noddings. Après avoir élaboré une analyse critique du paradigme moral que représente le dialogue « à la Socrate », notre thèse adresse la question de la portée éthique du dialogue dans le contexte spécifique de l’éducation morale contemporaine, en examinant trois théories éducatives spécialement influentes au Québec : celles de Lawrence Kohlberg, de John Wilson et de Matthew Lipman. Notre recherche présente un examen critique des conceptions du dialogue défendues dans ces théories. Elle propose une manière différente d’appréhender le dialogue moral qui devient, à travers l’éthique de la sollicitude, lié autant à un savoir être-en-relation qu’à un savoir raisonner. La thèse vient enfin démontrer la portée du « virage éthique » que la perspective relationnelle de sollicitude détermine pour éduquer au dialogue moral.

CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Sistemas descritos por Hamiltonianos do tipo Dirac são ubíquos. Surgindo em materiais como grafeno, isolantes topológicos ou recentemente nos semimetais de Weyl. Devido ao interesse tecnológico e acadêmico desses materiais, caracterizar suas propriedades é essencial. Uma abordagem matemática para efetuar o estudo de tais sistemas consiste em discretizar o Hamiltoniano no espaço das posições, mas tal abordagem esbarra no problema da duplicação de férmions. De forma breve, esse problema atesta pela impossibilidade de simulação de férmions livres não massivos em uma rede discreta sem que alguma simetria ou propriedade da Hamiltoniana seja quebrada. No presente trabalho demonstramos que tal problemática não deveria ser causa de preocupação para o estudo de sistemas na matéria condensada, pois podemos utilizar a simetria quebrada para confinar os portadores de carga no sistema para remover os estados duplicados. Tal remoção é conseguida com a inserção de um termo quadrático em relação ao momento, conhecido como massa de Wilson. Nesse sentido podemos inserir um termo de Wilson com quebra de simetria necessária para o confinamento, tornando o problema de duplicação de férmions irrelevante, essa relação não tinha sido notada até o presente trabalho, e recentes resultados na literatura erroneamente atribuem a massa de Wilson com a quebra de uma simetria de reversão temporal, o que não necessariamente é verdade. Nesse contexto além de abordar essa relação a presente dissertação objetiva também elucidar alguns mal entendimentos a respeitos das massas de Wilson, quiralidade e outras simetrias. Para validar nosso argumento central estudamos diversos sistemas de interesse e comparamos com os resultados na literatura. / Hamiltonians of Dirac type are ubiquitous. Appearing in materials such as graphene, topological insulators or recently in the Weyl semimetals. Due to the technological and academic interest of these materials, characterizing their properties is essential. A mathematical approach to study these systems consists of discretizing the Hamiltonian in the space of positions, but such an approach causes the problem of doubling fermions (FDP). We demonstrate the FDP should not be a cause of concern for the study of confined systems because we can use the broken symmetry to confine in the system to remove the duplicate states. Such removal is achieved by inserting a quadratic term with respect to the moment, known as the Wilson mass. In this sense we can insert a Wilson term with symmetry breaking required for confinement, rendering the fermion duplication problem irrelevant, this relationship had not been noticed until the present work, and recent literature results erroneously attribute Wilson’s mass to break of a symmetry of time reversal, which is not necessarily true. In this context, in addition to addressing this relationship, the present dissertation also aims to elucidate some misconceptions regarding the Wilson masses, chirality and other symmetries. In order to validate our central argument we study several systems of interest and compare it with the results in the literature. / Dissertação (Mestrado)

Cette thèse se divise en trois parties qui peuvent être toutes regroupées autour d'une même bannière : l'étude de structures algébriques reliées aux algèbres de type Askey–Wilson. Alors que dans la première partie on s'efforce d'obtenir des interprétations duales (au sens de Howe) de ces algèbres, dans les autres parties on étudie des généralisations de ces algèbres. Des dégénérations de l'algèbre de Sklyanin, générées par des blocs plus fondamentaux que ceux générant les algèbres de type Askey–Wilson, sont étudiées dans la deuxième partie et des généralisations de plus haut rang des algèbres de type Askey–Wilson sont étudiées dans la troisième partie. Dans la première partie, en invoquant la dualité de Howe, deux interprétations duales sont obtenues pour les algèbres de Racah, Bannai–Ito, Askey–Wilson, Higgs, Hahn, \(q\)-Hahn et dual \(-1\) Hahn. La façon dont la dualité de Howe opère est rendue explicite par l'examen de processus de réduction dimensionnelle. Un modèle superintégrable 2D de mécanique quantique superconforme dont l'algèbre de symétrie est celle de type dual \(-1\) Hahn est également introduit et solutionné. Dans la deuxième partie, des algèbres générées par des opérateurs de contiguïté et d'échelle encodant des propriétés de familles de polynômes sont étudiées. Ces opérateurs appartiennent à la classe des opérateurs de Sklyanin–Heun, qui peuvent être définis sur plusieurs grilles diverses. On découvre qu'ils génèrent des dégénérations de l'algèbre de Sklyanin. On démontre que les représentations irréductibles de dimension finie de ces algèbres ont pour base des familles de para-polynômes. Les grilles linéaires, quadratiques, exponentielles et d'Askey–Wilson sont étudiées et mènent respectivement aux polynômes orthogonaux des familles de para-Krawtchouk, para-Racah, \(q\)-para-Krawtchouk et \(q\)-para-Racah. Enfin, la façon dont les polynômes de para-Krawtchouk et d'autres familles de polynômes orthogonaux sont reliées aux représentations tridiagonales du plan de Jordan déformé est présentée. Dans la dernière partie, on explore des généralisations à plus haut rang pour les algèbres de Racah et Askey–Wilson. Pour ce faire, on étudie les réalisations de ces algèbres en termes de Casimirs intermédiaires. Le rôle de la matrice \(R\) tressée est élucidé : celle-ci permet de relier divers Casimirs intermédiaires entre eux par conjugaison. Un isomorphisme entre l'algèbre de skein du crochet de Kauffman de la sphère à 4 trous et l'algèbre engendrée par les Casimir intermédiaires dans \(U_q(\mathfrak{sl}_2)^{\otimes 3}\) est présenté et permet d'interpréter de façon diagrammatique la conjugaison par la matrice \(R\) tressée mentionnée ci-haut. Finalement, une présentation du centralisateur \(Z_n(\mathfrak{sl}_2)\) de \(U(\mathfrak{sl}_2)\) dans \(U(\mathfrak{sl}_2)^{\otimes n}\) par générateurs et relations est obtenue et on montre que ce centralisateur est isomorphe à un quotient (obtenu explicitement) de l'algèbre de Racah de plus haut rang \(R(n)\). / This thesis is divided in three parts which all orbit around the same theme: the study of algebraic structures related to the algebras of Askey–Wilson type. In the first part we obtain two interpretations that are dual in the sense of Howe for the algebras of Askey–Wilson type. Meanwhile, the other two parts are concerned with generalizations of these algebras. In the second part, we study degenerations of the Sklyanin algebra, which are built out of generators that are more fundamental than those of the Askey–Wilson algebra. In the last part, generalizations of the Askey–Wilson type algebras to higher rank are studied. In the first part, dual interpretations are obtained for the Racah, Bannai–Ito, Askey–Wilson, Higgs, Hahn, \(q\)-Higgs and dual \(-1\) Hahn algebras by invoking Howe duality. The way that this Howe duality operates is made explicit through the examination of a dimensional reduction procedure. A 2D superintegrable superconformal quantum mechanics model, whose symmetry algebra is the one of dual \(-1\) Hahn type, is also introduced and solved. In the second part, we study algebras that are generated by contiguity and ladder operators that encode properties of families of orthogonal polynomials. We show that these operators belong to the Sklyanin–Heun class of operators, which can be defined for various grids. We also show how their algebraic relations correspond to those of degenerations of the Sklyanin algebra. Then, we show how various families of para-polynomials support finite-dimensional irreducible representations of these degenerate algebras. From the linear, quadratic, exponential and Askey–Wilson grids, we are respectively led to the para-Krawtchouk, para-Racah, \(q\)-para-Krawtchouk and \(q\)-para-Racah polynomials. Later, we connect the para-Krawtchouk polynomials (and other families of orthogonal polynomials) to tridiagonal representations of the deformed Jordan plane. In the final part, we explore higher rank generalizations of the Racah and Askey–Wilson algebras. To that end, their realizations in terms of intermediate Casimir elements are studied. The role of the braided \(R\)-matrix is understood as follows: it connects various intermediate Casimir elements through conjugation. We obtain an isomorphism between the Kauffman bracket skein algebra of the four-punctured sphere and the algebra generated by the intermediate Casimir elements in \(U_q(\mathfrak{sl}_2)^{\otimes3}\). This leads to a diagrammatic interpretation of the conjugation by the braided \(R\)-matrix mentioned in the above. Lastly, a presentation of the centralizer \(Z_n(\mathfrak{sl}_2)\) of \(U(\mathfrak{sl}_2)\) in \(U(\mathfrak{sl}_2)^{\otimes n}\) by generators and relations is obtained and we show that this centralizer is isomorphic to a quotient (which we provide explicitly) of the higher rank Racah algebra \(R(n)\).

L’existence de physique au-delà du modèle standard semble de plus en plus évidente, notamment en raison d’observations d’anomalies dans plusieurs phénomènes. De plus, certains phénomènes tels que la matière noire, la gravité et l’asymétrie baryonique dans l’univers sont inexpliqués. Ce mémoire s’intéresse à la recherche de nouvelle physique à basse énergie par l’approche des EFT et se penche sur les prédictions à basse énergie d’une EFT en particulier : la SMEFT. Le premier article présenté s’intéresse aux anomalies présentes dans les données expérimentales liées aux mésons B et teste les prédictions de la SMEFT pour la désintégration b → cτν jusqu’à la dimension massive 6. Le but est de vérifier si la symétrie du modèle standard, soit SU(3)_C × SU(2)_L × U(1)_Y, est réalisée linéairement à haute énergie par la nouvelle physique. Le deuxième article détermine les relations de correspondance entre les opérateurs LEFT jusqu’à la dimension massive 6 et les opérateurs SMEFT jusqu’à la dimension massive 8. / The existence of physics beyond the Standard Model seems more and more obvious, partially because of observations of anomalies in many phenomena. Moreover, some phenomena such as dark matter, gravity and the baryon asymmetry in the universe are unexplained. This thesis addresses the search of New Physics at low energies using the EFT approach and looks into the predictions of low-energy predictions of one EFT in particular: SMEFT. The first paper presented addresses anomalies present in experimental data related to B mesons and tests the predictions of SMEFT for b → cτν decays up to mass dimension 6. The goal is to check if the Standard Model symmetry, being SU(3)_C × SU(2)_L × U(1)_Y, is linearly realized at high energy by the New Physics. The second paper determines the matching conditions between LEFT operators up to mass dimension 6 and SMEFT operators up to mass dimension 8.

Cette thèse est divisée en quatre parties qui portent sur les centralisateurs des algèbres quantiques \(U_q(\mathfrak{sl}_N)\), les polynômes biorthogonaux avec propriétés bispectrales, les polynômes bivariés de Griffiths, et les schémas d'association avec structures polynomiales bivariées. Le fil conducteur principal entre ces parties est l'algèbre d'Askey–Wilson. Dans la première partie, l'idée principale est de combiner l'algèbre du groupe des tresses avec l'algèbre d'Askey–Wilson dans des situations qui impliquent les centralisateurs de \(U_q(\mathfrak{sl}_2)\). Ainsi, on obtient des représentations du groupe des tresses en termes de polynômes orthogonaux de \(q\)-Racah par le biais de matrices \(R\) de \(U_q(\mathfrak{sl}_2)\), on obtient une interprétation de l'algèbre d'Askey–Wilson dans le cadre de la théorie topologique des champs de Chern–Simons avec groupe de jauge \(SU(2)\) ainsi que dans le cadre des invariants d'entrelacs associés à \(U_q(\mathfrak{su}_2)\), et on offre une description algébrique complète du centralisateur de \(U_q(\mathfrak{sl}_2)\) dans un produit tensoriel de trois représentations irréductibles identiques de spin quelconque. Dans une optique différente, on offre aussi une présentation algébrique de certaines algèbres de Hecke fusionnées qui décrivent des centralisateurs de \(U_q(\mathfrak{sl}_N)\). Dans la deuxième partie, on étudie deux familles de polynômes biorthogonaux par des méthodes algébriques, offrant une extension du tableau qui existe pour les polynômes orthogonaux classiques de type Askey–Wilson. Les deux familles considérées sont les polynômes \(R_I\) de type Hahn et les polynômes de Pastro. Dans les deux cas, l'idée est d'introduire un triplet d'opérateurs ayant une action tridiagonale et d'obtenir les polynômes comme solutions à deux problèmes aux valeurs propres généralisés provenant de ce triplet. On trouve les propriétés de bispectralité et de biorthogonalité des polynômes en se servant des opérateurs du triplet, et on détermine l'algèbre réalisée par les opérateurs. Dans la troisième partie, on caractérise deux familles de polynômes bivariés de Griffiths. La première famille est une généralisation des polynômes de Griffiths de type Krawtchouk qui dépend d'un paramètre \(\lambda\). On trouve leurs relations de bispectralité et leur biorthogonalité en utilisant les propriétés des polynômes de Krawtchouk à une variable. Les relations de contiguïté des polynômes univariés jouent un rôle essentiel dans les calculs. On utilise des méthodes semblables pour caractériser la deuxième famille, qui est formée de polynômes de Griffiths de type Racah. Ceux-ci sont orthogonaux. Dans la quatrième partie, on propose une généralisation bivariée des propriétés \(P\)- et \(Q\)-polynomiales pour les schémas d'association et de concepts reliés. Plusieurs exemples de schémas vérifiant la propriété \(P\)-polynomiale bivariée sont obtenus. On montre que les schémas de Johnson non-binaires ainsi que leurs analogues \(q\)-déformés, les schémas définis à partir d'espaces atténués, sont \(P\)- et \(Q\)-polynomiaux bivariés en étudiant les propriétés bispectrales des polynômes bivariés associés. Les structures algébriques reliées à ces schémas sont explorées. On propose aussi une généralisation multivariée des graphes distance-réguliers, et on montre que ceux-ci sont en correspondance avec des schémas \(P\)-polynomiaux multivariés. Finalement, on étudie une sous-classe de paires de Leonard de rang 2 qui font intervenir des polynômes bivariés factorisés. / This thesis is divided in four parts concerning centralizers of quantum algebras \(U_q(\mathfrak{sl}_N)\), biorthogonal polynomials with bispectral properties, bivariate Griffiths polynomials, and association schemes with bivariate polynomial structures. The main topic relating all these parts is the Askey–Wilson algebra. In the first part, the main idea is to combine the braid group algebra with the Askey–Wilson algebra in situations involving the centralizers of the quantum algebra \(U_q(\mathfrak{sl}_2)\). Hence, we obtain representations of the braid group in terms of \(q\)-Racah orthogonal polynomials using \(R\)-matrices of \(U_q(\mathfrak{sl}_2)\), we obtain an interpretation of the Askey–Wilson algebra in the framework of Chern–Simons topological quantum field theory with gauge field \(SU(2)\) as well as in the framework of link invariants associated to \(U_q(\mathfrak{su}_2)\), and we provide a complete algebraic description of the centralizer of \(U_q(\mathfrak{sl}_2)\) in the tensor product of three identical irreducible representations of any spin. In a different perspective, we also provide an algebraic presentation of some fused Hecke algebras, which describe some centralizers of \(U_q(\mathfrak{sl}_N)\). In the second part, we study two families of biorthogonal polynomials using algebraic methods, hence extending the picture that exists for the classical orthogonal polynomials of the Askey–Wilson type. The two families that we consider are the \(R_I\) polynomials of Hahn type and the Pastro polynomials. In both cases, the idea is to introduce a triplet of operators with tridiagonal actions and obtain the polynomials as solutions of two generalized eigenvalue problems involving this triplet. We find the bispectrality and biorthogonality properties of the polynomials using the operators of the triplet, and we determine the algebra realized by the operators. In the third part, we characterize two families of bivariate Griffiths polynomials. The first family is a generalization of the Griffiths polynomials of Krawtchouk type which depends on a parameter \(\lambda\). We find their bispectrality relations and their biorthogonality by using the properties of univariate Krawtchouk polynomials. The contiguity relations of the univariate polynomials play a key role in the computations. We use similar methods to characterize the second family, which is formed by Griffiths polynomials of Racah type. These are orthogonal. In the fourth part, we propose a bivariate generalization of the \(P\)- and \(Q\)-polynomial properties of association schemes and related concepts. Several examples of schemes satisfying the bivariate \(P\)-polynomial property are obtained. We show that the non-binary Johnson schemes and their \(q\)-deformed analogs, the schemes based on attenuated spaces, are bivariate \(P\)- and \(Q\)-polynomial by studying the bispectral properties of the associated bivariate polynomials. The algebraic structures related to these schemes are explored. We also propose a multivariate generalization of distance-regular graphs, and we show that these are in correspondence with multivariate \(P\)-polynomial schemes. Finally, we study a subclass of rank 2 Leonard pairs involving factorized bivariate polynomials.

In dieser Arbeit betrachten wir zwei Ansätze zur Untersuchung von Korrelationsfunktionen in eindimensionalen konformen Feldtheorien mit Defekten (dCFT1), insbesondere solche, die durch 1/2-BPS-Wilson-Linien-Defekte in den drei- und vierdimensionalen superkonformen Theorien definiert sind, die für die AdS/CFT-Korrespondenz relevant sind. Zunächst verwenden wir den analytischen konformen Bootstrap, um zwei Beispiele von Defektkorrelatoren auszuwerten. Der Vier-Punkt-Korrelator des Verschiebungs-Supermultipletts, das auf der 1/2-BPS-Wilson-Linie in der ABJM-Theorie eingefügt ist, wird bis zur dritten Ordnung in einer starken Kopplungsexpansion berechnet und reproduziert die expliziten Witten-Diagramm-Berechnungen erster Ordnung. Anschließend wird der Fünf-Punkt-Korrelator von 1/2-BPS-Operatoren, die auf der 1/2-BPS-Wilson-Linie in N=4 Super-Yang-Mills eingefügt sind, untersucht und in einer starken Kopplungsexpansion bis zur ersten Ordnung gebootstrapped. Anschließend werden die CFT1-Daten extrahiert, die bestätigen, dass das Mischen von Operatoren die anomale Dimension erster Ordnung nicht beeinflusst. Der zweite Ansatz betrachtet die allgemeine Struktur von Korrelatoren in effektiven Theorien in AdS2. Es werden alle skalaren n-Punkt-Kontakt-Witten-Diagramme für externe Operatoren mit ganzzahligem konformem Gewicht berechnet. Effektive Theorien in AdS2, die durch eine Wechselwirkungslagrange mit einer beliebigen Anzahl von Ableitungen definiert sind, werden dann betrachtet und mit Hilfe eines neuen Formalismus der Mellin-Amplituden für 1d-CFTs bis zur ersten Ordnung gelöst. Schließlich wird die diskretisierte Wirkung der Cusped-Wilson-Linie als alternative Möglichkeit zur Gewinnung nicht-perturbativer Daten vorgestellt: durch die Gitterfeldtheorie. / In this thesis, we consider two approaches to the study of correlation functions in one-dimensional defect Conformal Field Theories (dCFT1), in particular those defined by 1/2-BPS Wilson line defects in the three- and four-dimensional superconformal theories relevant in the AdS/CFT correspondence. In the first approach, we use the analytic conformal bootstrap to evaluate two examples of defect correlators. The four-point correlator of the displacement supermultiplet inserted on the 1/2-BPS Wilson line in ABJM theory is computed to the third order in a strong-coupling expansion and reproduces the explicit first-order Witten diagram calculations. The CFT1 data are then extracted from this correlator, and the operator mixing is solved at first order. Consequently, all-order results are derived for the part of the correlator with the highest logarithm power, uniquely determining the double-scaling limit. Then, the five-point correlator of 1/2-BPS operators inserted on the 1/2-BPS Wilson line in =4 super Yang-Mills are studied. The superblocks are derived for all channels of the OPE, and the five-point correlator is bootstrapped to first order in a strong coupling expansion. The CFT1 data are then extracted, confirming that operator mixing does not affect the first-order anomalous dimension. The second approach considers the general structure of correlators in effective theories in AdS2. All scalar n-point contact Witten diagrams for external operators of integer conformal weight are computed. Effective theories in AdS2 defined by an interaction Lagrangian with an arbitrary number of derivatives are then considered and solved to first order using a new formalism of Mellin amplitudes for 1d CFTs. Finally, the cusped Wilson line discretised action is presented as an alternative way to obtain non-perturbative data: through Lattice Field Theory.

Diese Arbeit wird durch die AdS/CFT Korrespondenz, sowie durch die Dualität zwischen lichtartigen, polygonalen Wilsonschleifen und Gluonenstreuamplituden in N=4 Super-Yang-Mills-Theorie motiviert. Bei starker Kopplung haben lichtartige, polygonale Wilsonschleifen und Gluonenstreuamplituden eine Beschreibung über raumartige Minimalflächen in AdS5. Wir benutzen eine Pohlmeyerreduktion, um eine Klassifikation aller raumartigen Minimalflächen in AdS3xS3 mit flachen Projektionen herzuleiten. Diese Klassifikation enthält neun verschiedene Klassen von Flächen. Dabei treten raumartige, zeitartige und degenerierte AdS3-Projektionen auf. Bei denjenigen Lösungen, die einen geschlossenen, polygonalen und lichtartigen Rand besitzen, berechnen wir den regularisierten Flächeninhalt. Bei schwacher Kopplung erfüllen lichtartige, polygonale Wilsonschleifen und Gluonenstreuamplituden den um eine Remainderfunktion korrigierten BDS-Ansatz. Wir präsentieren eine Technik, die auf einer Renormierungsgruppengleichung für selbstschneidende Wilsonschleifen beruht, mit der wir die Divergenzen der Remainderfunktion in diesem Limes berechnen können. Mittels dieser Technik analysieren wir zwei Arten des Selbstschnittes. Im Falle des Selbstschnittes zwischen zwei Ecken berechnen wir die führenden Divergenzen bis zur vierten Schleifenordnung. Beim Selbstschnitt zwischen zwei Kanten berechnen wir die führenden und nächstfolgenden Divergenzen bis zur vierten Schleifenordnung und präsentieren eine analytische Fortsetzung in die Region der Euklidischen Wilsonschleifen und sagen bestimmte Terme vorher, die in dem unbekannten analytischen Ausdruck für die Remainderfunktion enthalten sein müssen. / This thesis is motivated by the AdS/CFT correspondence and the duality between gluon scattering amplitudes and light-like polygonal Wilson loops in N=4 super Yang-Mills theory. At strong coupling light-like polygonal Wilson loops and gluon scattering amplitudes have a description in terms of space-like minimal surfaces in AdS5. We use a Pohlmeyer reduction to derive a classification of all space-like minimal surfaces in AdS3xS3 that have flat projections. The classification consists of nine different classes and contains space-like, time-like and degenerated AdS3 projections. For solutions that admit a closed light-like polygonal boundary we calculate the regularized area. At weak coupling light-like polygonal Wilson loops and gluon scattering amplitudes obey the BDS Ansatz corrected by a remainder function. We present a renormalisation group equation technique using self-crossing Wilson loops to extract the divergences of the remainder function in this limit. Using this technique we analyse two different types of self-crossing. We present the leading and sub-leading divergences up to four loops for a crossing between two edges and the leading divergences for a crossing between two vertices. For a crossing between two edges we present an analytic continuation to the euclidean regime to predict certain terms that have to occur in the unknown analytic expression of the remainder function.

We studied the structural instabilities of one-dimensional (1D) and quasi-one-dimensional (Q1D) electron-phonon systems at low temperature through two models, SuSchrieffer-Heeger (SSH) and molecular crystal (CM) with and without spin. The phase diagrams are obtained using a Kadanoff-Wilson renormalization group approach (GR). For the 1D half-filled system the study of the frequency dependence of the electronic gap allowed us to connect continuously the two limits, adiabatic and non-adiabatic. The Peierls and Cooper channels interference and the quantum fluctuations reduce the gap. A regime change occurs when the frequency becomes of the order of mean field gap, marking a quantum-classical crossover that is the Kosterlitz-Thouless type. At this level, the effective coupling behaves in power law function on frequency. For the case with spin, a gapped Peierls state is maintained in the non-adiabatic limit, while for the case without spin, the system transits to ungapped disordered state, namely the Luttinger liquid stat (LL). For the SSH model without spin, the GR confirms the existence of a threshold phonon coupling beyond which the gap is restored. The study of the rigidities of the two models without spin allowed us to trace the main features of the LL state predicted by the bosonization method. The study of the Holstein-Hubbard model has allowed us not only to reproduce the phase diagrams already obtained by the Monte Carlo method, but to highlight two additional phases, namely, free fermions phase and the bond charge-density-wave phase. We have extended this study to the quarter-filled Q1D Peierls systems at finite temperature. Within the SSH model, an unconventional superconducting phase with spin singlet symmetry SS-s emerges at low temperature when the deviation to the perfect nesting of the Fermi surface is strong enough. Peierls-SS transition is characterized by the presence of a quantum critical point at low frequency and by a power law behavior of the transition temperature as a function of frequency with an exponent identical to one of 1D system. This exponent which universality has been verified contrasts with the BCS result. Coulomb interactions have been introduced through the study of the extended SSH-Hubbard model. The extension of this work to half-filled SSH and CM cases was also performed.

This work reinterprets the idea of progress at the heart of Woodrow Wilson’s liberal internationalism through the lens of secularization theory, which holds that modern philosophies of progress stand on religious foundations and represent secularized vestiges of biblical eschatology. Previous applications of this insight reveal a selective pattern: Whereas totalitarian and illiberal narratives of progress such as Nazism and Marxism-Leninism have received lavish attention and spawned extensive political religions literature, liberal progressivism has been ignored. This dissertation rectifies this neglect. Initial chapters present the biblical conception of history as the myth of salvation, introduce secularization through the writings of Karl Löwith and Hans Blumenberg, respectively its principal proponent and main critic, and test the limits of the concept to confirm its applicability to liberal progressivism. The main part aims secularization theory at Wilson’s idea of progress in the broader context of American liberal thought. From the 17th-century Puritan vision of a “city upon a hill” to the 19th-century doctrine of “manifest destiny”, biblical eschatology defined the way Americans envisioned history and their role in it, giving rise to a sort of liberal-republican millennialism. Wilson was no exception: Considering faith essential to authentic knowledge, he regarded history as a providential process, the United States as a divinely appointed redeemer nation, and himself as a Christian statesman performing God’s work in a fallen world. His foreign policy was fundamentally a religious mission to transform international relations according to the Bible, thereby fulfilling the prophecy of salvation. The dissertation demonstrates the eschatological foundations of his statecraft through specific examples and draws attention to their illiberal and totalizing implications. Final passages note the enduring relevance of Wilson’s principles and, based on their reinterpretation in this work, reflect critically on their suitability as a guide for future American foreign policy.

The Meisner Technique emerged as a part of the realist, modern theatre of the early-Twentieth Century and extended its influence through the rest of that century, including the 1960s and 1970s when there was an explosion of various forms of postmodern performance. This work will demonstrate that while Meisner’s Technique is a part of the paradigm of modern, realist theatre, it simultaneously challenges this ideology with disruptive processes of the sort that postmodern performance instigates. It is the thesis of this work that the Meisner Technique operates according to a set of phenomenologically-aligned imperatives that create strong resonances with certain forms of postmodern performance. This establishes the dynamic wherein the Meisner Technique is able to enter into discourse with instances of the postmodern paradigm of performance. In the first three chapters I will conduct in-depth analyses of Meisner actors’ relationships with their environment, their fellow performers, and their actions from a range of phenomenological perspectives. In the fourth chapter I will apply the conclusions of these analyses to the operation of the Meisner Technique within the paradigm of modern, realist theatre. In the fifth chapter I will set a backdrop to the postmodern field and suggest the issues from this tradition with which the Meisner Technique might resonate. Chapters Six, Seven, and Eight each take one example of an artist from the postmodern field, Richard Foreman, Michael Kirby, and Robert Wilson respectively, establishes their own particular context, and suggests those processes relating to acting/performing technique that might provoke the most productive exchanges. This juxtaposition suggests the places between the practices where discourse might take root and suggests the beginnings of such dialogues.