Conselho Nacional de Desenvolvimento Científico e Tecnológico / Neste trabalho, os efeitos de um campo magnético oblíquo externo no modelo de Gross- Neveu (2+1)-dimensional, que inclui as componentes paralela e perpendicular do campo em relação ao sistema, são estudados no contexto da simetria quiral e discreta do modelo. Nosso principal interesse está nos efeitos deste campo sobre o diagrama de fase do sistema, onde também incluímos os efeitos combinados de temperatura e potencial químico. Os diagramas de fase são obtidos através do potencial efetivo a 1 loop para o modelo, derivado em primeira ordem na expansão 1=N. Transições de fase relevantes que podem ser estudadas através deste modelo são, por exemplo, metal-isolante em matéria condensada e na teoria quântica de campos de férmions planares em geral. A relação entre a transição de fase com quebra da simetria quiral e discreta e o surgimento de um gap (ou a presença de um valor esperado no vácuo do campo escalar diferente de zero), como função do campo magnético oblíquo, é analisada em detalhes. / In this work, the effects of an external oblique magnetic field in the (2+1)-dimensional Gross-Neveu model, and that therefore includes both parallel and perpendicular components of the applied field, are studied in the context of the models discrete chiral symmetry. Our main concern is in the effects of such a field in the systems phase diagram and that also includes the combined effects of temperature and chemical potential. The phase diagrams are obtained through the one-loop effective potential for the model, derived in the leading order in the 1=N expansion Relevant phase transitions that can be studied through this model are, for example, metal-insulator ones in condensed matter and in the quantum field theory of planar fermions in general. The relation between the phase transition with (discrete) chiral symmetry breaking and the emergence of a gap (or the presence of a chiral nonvanishing vacuum expectation value) in the planar fermionic system, as a function of the external oblique magnetic field, is analyzed in details.

Made available in DSpace on 2016-08-18T18:19:25Z (GMT). No. of bitstreams: 1 Josberg Silva Rodrigues.pdf: 647762 bytes, checksum: 76e44a5c4743594c8862ff4d8b22704c (MD5) Previous issue date: 2009-04-30 / FUNDAÇÃO DE AMPARO À PESQUISA E AO DESENVOLVIMENTO CIENTIFICO E TECNOLÓGICO DO MARANHÃO / In this work we study the effects of the spontaneous breaking of Lorentz symmetry on black body radiation phenomenon in the context of the Maxwell-Caroll-Field-Jackiw (MCFJ) model. The MCFJ model is the electromagnetic CPT-odd sector of the standard model extension and, it presents for a purely space-like background a positive-definite hamiltonian. Firstly, we study the Maxwell electrodynamics by analyzing its hamiltonian structure following the Dirac s procedure for constrained systems. Then, we calculate the partition function via the path integrals formalism and consequently we obtain its thermodynamic properties such as: energy density, radiation pressure and the entropy. Afterwards, we apply the same procedure to find the partition function of the MCFJ model and we observe how the spectrum of black body changes due to the breaking of the CPT and Lorentz symmetries. We show that if the cosmic microwave background (CMB) radiation is described by this model, it shows an angular anisotropy in the energy density distribution. We also give, at leading order in the Lorentz violating parameter, the contributions of the Lorentz breaking for the Planck s radiation and the Stefan-Boltzmann laws. The Lorentz-violating (LV) corrections for the Planck s law is non-linear in the frequency and for the Stefan-Boltzmann law is quadratic in the temperature. Using our results, we set upper limits for the LV parameter by analyzing the Stefan-Boltmann law and the CMB anisotropy but it is shown that they are much less stringents that those obtained by birefringence or polarization analysis of light. / Esta dissertação aborda os efeitos da quebra espontânea da simetria de Lorentz sob a radiação do corpo negro no contexto da eletrodinâmica de Maxwell-Carroll-Field-Jackiw (MCFJ). O modelo MCFJ advém do setor CPT-ìmpar do modelo padrão estendido e apresenta uma hamiltoniana positiva-definida somente para um campo de fundo puramente tipo-espaço. O estudo começa pela eletrodinâmica de Maxwell realizando uma análise de sua estrutura hamiltoniana através do procedimento de Dirac para sistemas vinculados. Após essa análise, calcula-se a função de partição via o formalismo de integração funcional e obtendo consequentemente suas propriedades termodinâmicas relevantes como: densidade de energia, pressão de radiação e a entropia do sistema. Na segunda parte, seguindo um procedimento similar encontramos a função de partição do modelo MCFJ. Observa-se que o espectro de energia do corpo negro sofre alteração devido à quebra da invariância de Lorentz e da simetria CPT. Mostramos que se a radiação cósmica de fundo (RCF) for descrita por esse modelo desponta uma anisotropia na distribuição de densidade de energia. Também, mostramos que a lei de radiação de Planck e a lei de Stefan Boltzmann são afetadas pela introdução do campo externo responsável pela quebra de Lorentz. Tais modificações no caso da lei de Planck são não-lineares na frequência e na lei de Stefan-Boltzmann são quadráticas na temperatura. Usando esses resultados e os dados experimentais da constante de Stefan-Boltzmann e os dados referentes a anisotropia da radiação cósmica de fundo, estipulamos limites superiores para a magnitude do parâmetro da VL. Contudo, os limites obtidos são menos restritivos que os obtidos pela análise do fenômeno da birrefrigência.

We study Cheeger-Simons differential characters in order to define higher form U(1) gauge fields and their Wilson lines. We then go on to define generalized global symmetries. This is a topological formulation of symmetries which has interesting consequences when the charged operators extend through space. Our main source of such charged operators are the generalized Wilson lines. A higher form Noether theorem and a Ward identity are given for transformations of Wilson lines. As examples of quantum field theories with generalized symmetries we cover Sigma models, Maxwell theory and BF-theory. These are examples of Z, U(1) and Zn symmetries respectively. Finally we discuss spontaneous symmetry breaking for higher dimensional symmetries and a Goldstone theorem is provided. These massless Goldstone bosons are shown to have internal structure corresponding to non-zero spin. The photon is identified as the spin one Goldstone boson in QED. Our review of generalized symmetries is more formal than the ones in other papers. This makes various points explicit and leads to general selection rules. Many results of previous papers are reproduced in detail.

L’étude des symétries d’un système peut en révéler de nombreuses propriétés physiques. La brisure, spontanée ou non, d’une de ces symétries implique alors d’importantes conséquences sur le comportement du système. On le voit dans la description actuelle de la physique des particules, avec notamment la création de la masse, ou dans la physique des solides, domaine de cette thèse, avec l’apparition de phases aux propriétés diverses, comme le magnétisme ou la supraconductivité. Le présent travail étudie par spectroscopie de photoémission résolue en angle (ARPES) les effets d’une brisure de symétrie dans deux systèmes différents : le système de fermions lourds URu2Si2 et l’oxyde de métal de transition (TMO) KTaO3. Le cristal d’URu2Si2 passe d’une phase paramagnétique pour T>THO, sujette à la cohérence de Kondo, vers la phase dite d’ordre caché pour T<THO, avec THO ≈ 17.5 K, brisant potentiellement plusieurs symétries. Bien qu’il y a presque trente ans que cettetransition de phase fut mesurée expérimentalement, aucun modèle théorique n’a encore réussi à faire consensus dans la communauté. Malgré une caractérisation expérimentale désormais très poussé de ce système, des informations résolues en angle manquent cruellement pour la compréhension de cette mystérieuse phase. Ce travail de thèse utilise donc des installations ARPES pour mettre en évidence, entre autre, le gap d’ordre caché, d’une amplitude inférieure à 10 meV. Nous montrons que ces mesures s’accordent avec plusieurs travaux expérimentaux précédents. Finalement, nous trouvons de fortes similarités entre les dispersions mesurées et celles calculées par LSDA, soulignant toutefois la nécessité d’introduire une renormalisation importante des masses effectives. Ce résultat contraint fortement les futures modélisations du comportement électronique de l’URu2Si2, tranchant sur l’approche à adopter.Contrairement au dernier système, où nous étudions une transition de phase, dans le tantalate de potassium KTaO3, notre attention se porte sur la brisure de symétrie de translation provoquée par la surface (111). Faisant suite à des mesures de transport qui revélèrent l’existence d’un gaz d’électron bidimensionnel (2DEG) à l’interface d’une hétérostructure de deux TMOs isolants de bandes, notre groupe mesura, plus tard, des 2DEGs aux surfaces (001) nues de SrTiO3 et de KTaO3, par ARPES. C’est dans la continuité de ces résultats que se place le présent travail, avec le désir d’élargir les caractéristiques de ces 2DEGs. Ainsi, poussé par la prédiction théorique d’état au caractère topologique non-trivial, nous apportons l’évidence d’un 2DEG à la surface (111) de KTaO3. Nous modélisons ensuite avec succès sa dispersion particulière grâce à des calculs de liaisons fortes. Ce travail constitue une étape dans la possible mise en évidence d’états au caractère topologique non-trivial dans les TMOs. / Several physical properties of a system can be understood by looking at the symmetries involved. Breaking of a symmetry affects the behavior of the system, regardless ifit happens spontaneously or not. This is observed with the emergence of the mass inparticle physics models, or with the diverse phases arising in condensed matter systems,as magnetism or superconductivity. Using angle-resolved photoemission spectroscopy (ARPES), this work studies theeffects of a symmetry breaking for two different systems : the heavy fermion systemURu2Si2 and the transition metal oxide (TMO) KTaO3. In URu2Si2, a transition occurs from a paramagnetic phase at T>THO to the hiddenorder phase at T<THO, with THO ≈ 17.5 K. This new order potentially breaks several symmetries. Although this transition was measured almost thirty years back, usingelectrical transport, no theoretical model could yet bring a consensus in the community. Since then, various characterizations of this system have been realized, howevermomentum-resolved informations are still missing to help unravel this mystery. Thus,during this thesis, we used state-of-the-art ARPES setups to measure several gaps located at different points in the Brillouin zone, and with amplitudes below 10 meV. Someof them are related to the Kondo coherence, and one is the hidden order gap. We showthat these measurements are consistent with previous experimental works. Finally, weobserved that our measurements differ from LSDA calculations solely by a renormalization of the effective masses by, at least, a factor 10 close to the Fermi level. Taking intoaccount some interactions, such as electronic ones, could lead to a more accurate model.Our measurements provide the constraints for this possible modeling. Unlike the transition we just described, the symmetry breaking in potassium tantalate KTaO3 is not spontaneous. In this system, we look at the (111) surface, wherethe translation symmetry is broken. A metallic two-dimensional electron gas (2DEG)has been measured in 2004 by Ohtomo at the interface between two insulating TMOs :strontium titanate SrTiO3 and lanthanum aluminate LaAlO3. The possible electronicapplications of exotic properties in TMOs, resulting from the d orbitals, has brought anew wave of activity to this topic. Later, our group measured 2DEGs at the (001) baresurfaces of SrTiO3 and KTaO3. Following these results, we wished to tailor the characteristic of such 2DEGS. Led by the theoretical prediction of states with non-trivialtopological character, we are presenting the evidence of a 2DEG at the (111) surface ofKTaO3. We also discuss its dispersion and introduce a tight binding calculation modelsuccessfully. This work is a step towards the realization of non-trivial topological statesin transition metal oxides.

The scattering of electroweak gauge bosons is closely connected to the electroweak gauge symmetry and its spontaneous breaking through the Brout-Englert-Higgs mechanism. Since it contains triple and quartic gauge boson vertices, the measurement of this scattering process allows to probe the self-interactions of weak bosons. The contribution of the Higgs boson to the weak boson scattering amplitude ensures unitarity of the scattering matrix. Therefore, the scattering of massive electroweak gauge bosons is sensitive to deviations from the Standard Model prescription of the electroweak interaction and of the properties of the Higgs boson. At the Large Hadron Collider (LHC), the scattering of massive electroweak gauge bosons is accessible through the measurement of purely electroweak production of two jets and two gauge bosons. No such process has been observed before. Being the channel with the least amount of background from QCD-mediated production of the same final state, the most promising channel for the first measurement of a process containing massive electroweak gauge boson scattering is the one with two like-charge W bosons and two jets in the final state. This thesis presents the first measurement of electroweak production of two jets and two identically charged W bosons, which yields the first observation of a process with contributions from quartic gauge interactions of massive electroweak gauge bosons. An overview of the most important issues in Monte Carlo simulation of vector boson scattering processes with current Monte Carlo generators is given in this work. The measurement of the final state of two jets and two leptonically decaying same-charge W bosons is conducted based on proton-proton collision data with a center-of-mass energy of √s = 8 TeV, taken in 2012 with the ATLAS experiment at the LHC. The cross section of electroweak production of two jets and two like-charge W bosons is measured with a significance of 3.6 standard deviations to be σ(W± W±jj−EW[fiducial]) = 1.3 ± 0.4(stat.) ± 0.2(syst.) fb in a fiducial phase space region selected to enhance the contribution from W W scattering. The measurement is compatible with the Standard Model prediction of σ(W±W± jj−EW[fiducial]) = 0.95 ± 0.06 fb. Based on this measurement, limits on anomalous quartic gauge couplings are derived. The effect of anomalous quartic gauge couplings is simulated within the framework of an effective chiral Lagrangian unitarized with the K-matrix method. The limits for the anomalous coupling parameters α4 and α5 are found to be −0.14 < α4 < 0.16 and −0.23 < α5 < 0.24 at 95 % confidence level. Furthermore, the prospects for the measurement of the electroweak production of two same-charge W bosons and two jets within the Standard Model and with additional doubly charged resonances after the upgrade of the ATLAS detector and the LHC are investigated. For a high-luminosity LHC with a center-of-mass energy of √s = 14 TeV, the significance of the measurement with an integrated luminosity of 3000 fb^−1 is estimated to be 18.7 standard deviations. It can be improved by 30 % by extending the inner tracking detector of the atlas experiment up to an absolute pseudorapidity of |η| = 4.0.

Title: Electroweak symmetry breaking by dynamically generated masses of quarks and leptons Author: Adam Smetana Department: Institute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles University Supervisor: Ing. Jiří Hošek, DrSc., Department of Theoretical Physics, Nuclear Physics Institute, Academy of Sciences of the Czech Republic Abstract: The aim of the thesis is to study models of the electroweak symmetry breaking caused by dynamically generated masses of quarks and lep- tons. (1) We perform the basic analysis whether the main underlying idea, that the masses of only known fermions can provide the elec- troweak symmetry breaking, is actually feasible. For that we elaborate a two-composite-Higgs-doublet model of the top-quark and neutrino condensation. The model suggests rather large number, O(100), of right-handed neutrinos. (2) We analyze the model of strong Yukawa dynamics where the dynamical fermion mass generation is provided by exchanges of new elementary massive complex doublet scalar fields. We focus on solving the coupled Schwinger-Dyson equations for fermion and scalar self-energies by means of approximative methods. We doc- ument that strongly hierarchical mass spectra can be reproduced. (3) We elaborate the flavor gauge model where the dynamical fermion mass...

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Cette thèse présente une étude des applications des groupes de réflexion finis aux problems liés aux réseaux bidimensionnels et aux polytopes tridimensionnels. Plusieurs familles de fonctions orbitales, appelées fonctions orbitales de Weyl, sont associées aux groupes de réflexion cristallographique. Les propriétés exceptionnelles de ces fonctions, telles que l’orthogonalité continue et discrète, permettent une analyse de type Fourier sur le domaine fondamental d’un groupe de Weyl affine correspondant. Dans cette considération, les fonctions d’orbite de Weyl constituent des outils efficaces pour les transformées discrètes de type Fourier correspondantes connues sous le nom de transformées de Fourier–Weyl. Cette recherche limite notre attention aux fonctions d’orbite de Weyl symétriques et antisymétriques à deux variables du groupe de réflexion cristallographique A2. L’objectif principal est de décomposer deux types de transformations de Fourier–Weyl du réseau de poids correspondant en transformées plus petites en utilisant la technique de division centrale. Pour les cas non cristallographiques, nous définissons les indices de degré pair et impair pour les orbites des groupes de réflexion non cristallographique avec une symétrie quintuple en utilisant un remplacement de représentation-orbite. De plus, nous formulons l’algorithme qui permet de déterminer les structures de polytopes imbriquées. Par ailleurs, compte tenu de la pertinence de la symétrie icosaédrique pour la description de diverses molécules sphériques et virus, nous étudions la brisure de symétrie des polytopes doubles de type non cristallographique et des structures tubulaires associées. De plus, nous appliquons une procédure de stellation à la famille des polytopes considérés. Puisque cette recherche se concentre en partie sur les fullerènes icosaédriques, nous présentons la construction des nanotubes de carbone correspondants. De plus, l’approche considérée pour les cas non cristallographiques est appliquée aux structures cristallographiques. Nous considérons un mécanisme de brisure de symétrie appliqué aux polytopes obtenus en utilisant les groupes Weyl tridimensionnels pour déterminer leurs extensions structurelles possibles en nanotubes. / This thesis presents a study of applications of finite reflection groups to the problems related to two-dimensional lattices and three-dimensional polytopes. Several families of orbit functions, known as Weyl orbit functions, are associated with the crystallographic reflection groups. The exceptional properties of these functions, such as continuous and discrete orthogonality, permit Fourier-like analysis on the fundamental domain of a corresponding affine Weyl group. In this consideration, Weyl orbit functions constitute efficient tools for corresponding Fourier-like discrete transforms known as Fourier–Weyl transforms. This research restricts our attention to the two-variable symmetric and antisymmetric Weyl orbit functions of the crystallographic reflection group A2. The main goal is to decompose two types of the corresponding weight lattice Fourier–Weyl transforms into smaller transforms using the central splitting technique. For the non-crystallographic cases, we define the even- and odd-degree indices for orbits of the non-crystallographic reflection groups with 5-fold symmetry by using a representation-orbit replacement. Besides, we formulate the algorithm that allows determining the structures of nested polytopes. Moreover, in light of the relevance of the icosahedral symmetry to the description of various spherical molecules and viruses, we study symmetry breaking of the dual polytopes of non-crystallographic type and related tube-like structures. As well, we apply a stellation procedure to the family of considered polytopes. Since this research partly focuses on the icosahedral fullerenes, we present the construction of the corresponding carbon nanotubes. Furthermore, the approach considered for the non-crystallographic cases is applied to crystallographic structures. We consider a symmetry-breaking mechanism applied to the polytopes obtained using the three-dimensional Weyl groups to determine their possible structural extensions into nanotubes.

Dans cette thèse, nous nous intéressons à certains aspects concernant les phénomènes hadroniques à basse énergie sous 1 GeV, en dessous de laquelle la symétrie chirale de la Chromodynamique Quantique (QCD) est spontanément brisée. En dessous de cette échelle d'énergie, le spectre de QCD se réduit à un octet de mésons légers pseudo-scalaires (π, K and η). Mais à cause du confinement, QCD sous 1 GeV devient hautement non perturbative – il n'est donc plus possible de décrire à basse énergie la dynamique de ces mésons en termes de gluons et de quarks (ici seuls les quarks légers u, d et s sont concernés). Deux alternatives principales à cet obstacle majeur existent néanmoins: la QCD sur réseau ainsi que les Théories Effectives des Champs. La QCD sur réseau consiste à calculer de manière numériques les diverses observables hadroniques, alors que les théories effectives permettent de nouveau une approche analytique (et perturbative) adaptée à une échelle d'énergie donnée. Dans le cas de QCD à basse énergie, c'est la Théorie Chirale des Perturbations (ChiPT) qui joue le rôle de théorie effective. Cette théorie peut être construite à partir de deux saveurs de quarks légers (u et s) ou trois (u,d, et s). Il est alors possible d'utiliser certains résultats de calculs sur réseau (ainsi que certains résultats expérimentaux) afin d'extraire des valeurs numériques pour les divers paramètres libres que contient la théorie chirale. Il fut néanmoins observé que le développement en séries chirales de quelques observables hadroniques sont numériquement “malades” dans le cadre de la théorie à trois saveurs. En effet, des travaux antérieurs montrent qu'il pourrait exister une possible compétition numérique entre l'Ordre Dominant (LO) et l'Ordre Sous-Dominant (NLO): en place de la hiérarchie usuelle LO>>NLO, l'équivalence LO~NLO prévalerait. La partie principale de la thèse consiste ainsi à la description et l'utilisation d'une version alternative de ChiPT, nommée Théorie Chirale des Perturbations Ressommée (ReChiPT ). Quelques observables hadroniques de basse energie sont calculées puis étudiées dans ce cadre “ressommé”, puis nous procédons à l'ajustement de certaines données de QCD sur réseau obtenues par des simulations à 2+1 quarks dynamiques sur ces observables exprimées en ReChiPT: les constantes de désintégrations et les masses de l'octet (π, K, η), ainsi que les facteurs de forme Kl3. Nous testons ensuite la validité de notre assertion concernant la possible compétition numérique observée dans les séries chirales. Enfin, dans la dernière partie, nous discutons plusieurs aspects analytiques et numériques concernant certaines quantités topologiques liées de manière intrinsèque à la très complexe structure du vide de QCD, dans le cadre de ChiPT (ressommé), et nous confrontons de nouveau cette étude à des données réseau 2+1. / In this thesis, we focus on some aspects concerning hadronic phenomena at low energy, below 1 GeV, under which the spontaneous breaking of chiral symmetry takes place. Under this scale, the spectrum of Quantum Chromodynamics reduces to an octet of light pseudo-scalar mesons (π, K and η). But because of the confinement property, QCD under 1 GeV is highly non-perturbative, it is thus not possible to describe at low energy the dynamics of these mesons in terms of gluons and quarks (in that case the three light quarks u,d, and s). Two main alternatives exist to circumvent this major obstacle: Lattice QCD and Effective Field Theories. Lattice QCD is concerned with the numerical computations of various hadronic observables, while Effective Field Theories correspond to analytical frameworks adapted to a particular energy scale. In the case of QCD at low energy, this role is devoted to Chiral Perturbation Theory (ChiPT). This theory can be built either from two quark flavours (u and d), or three (u,d, and s). Using the numerical results from Lattice QCD, it is possible to obtain numerical values for the unknown parameters that ChPT contains. It was however observed that the series expansions of hadronic observables stemming from ChiPT calculations do not “behave well” numerically in the three-flavour case. Indeed, previous works shown that there could exists at the numerical level a competition between the Leading and the Next-to- Leading order (LO and NLO); i.e., instead of the usually expected hierarchy LO>>NLO, one would have LO~NLO. The main part of the thesis work consists in the description and the use of a modified version of ChiPT allowing this numerical competition in the chiral series that was called “Resummed ChiPT”. Within this “Resummed” framework, we proceed to fitting data from 2+1 lattice calculations to hadronic observables computed in ChiPT: decay constants and masses of π, K and η, and Kl3 form factors, and check the consistency of our claim about the numerical competition in ChiPT expansions. In the last part, we discuss topological quantities that are intrinsically tied to the very complex structure of the QCD vacuum, in the (resummed) ChiPT framework and in the light of 2+1 lattice data, in their analytical and numerical aspects.

See file appended.