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This thesis describes the neutron scattering measurements of magnetic excitations in spin-chains and ladders. The first part discusses an experimental investigation of the copper oxide family Sr₁₄Cu₂₄O₄₁ composed of edge-sharing chains and spin-ladders. The study of La₄Sr₁₀Cu₂₄O₄₁ comprises a slightly hole-doped chain and an undoped ladder structure where the chain can be modeled by a ferromagnetic nearest and an antiferromagnetic next-nearest neighbor coupling. The hole effects are apparent in gaps in the dispersion relation and can be described by a charge-density wave agreeing with the commensuration of the dispersion. Investigating the undoped ladder establishes the exchange constants including a cyclic exchange manifested by the two-magnon continuum and the suppression of the S = 1 bound mode. An orbital consideration provides an explanation for the exchanges including the different sizes of rung and leg coupling. The excitation spectrum of the doped ladder in Ca₂.₅Sr₁₁.₅Cu₂₄O₄₁ can be described by a direct comparison with the undoped ladder and the differences consisting of a higher energy mode and subgap scattering can be successfully modeled by the charge spectrum of the ladder calculated from the free electron model. The second part of the thesis investigates the alternating chain material Cu(NO₃)₂ · 2.5D2O and establishes the gapped one-magnon dispersion, the two-magnon continuum and for the first time the S =1 bound mode. Applying magnetic field drives the system through two critical field transitions, condensation of magnons into the ground state and saturation. The modes beyond saturation can be modeled by spin wave theory and the excitations at the first critical field follow Luttinger Liquid behavior. Additionally investigated are the temperature effects with the excitations being of a different nature but containing the signature of a strong correlated system. For an outlook the measurements including temperature and field are provided with further theoretical descriptions necessary.

The imaginary part of the retarded self energy is of particular interest as it contains a lot of physical information about particle interactions. In higher order loop diagrams the calculation become extremely tedious and if we have to do the same at finite temperature, it includes an extra dimension to the difficulty. In such a condition we require to switch between bases and select the best basis for a particular diagram. We have shown in our calculation that in higher order loop diagrams, at finite temperature, the R/A basis is most convenient on summing over the internal vertices and very efficient on calculating some particular diagrams while the result is most easily interpretable in the Keldysh basis for most other complex diagrams. / February 2010

Orientador: Julio Marny Hoff da Silva / Banca: Saulo Henrique Pereira / Banca: Marco André Ferreira Dias / Banca: José Abdalla Helayel-Neto / Banca: Alexis Roa Aguirre / Resumo: Na presente tese apresentaremos de forma detalhada o estudo sistemático de uma teoria quântica com férmions de dimensão de massa um que obedecem as estatísticas de Fermi-Dirac, abordando essencialmente sua construção, quantização do campo, análise dos observáveis físicos e aplicações quânticas. Forneceremos todos os detalhes de uma descoberta teórica inesperada da partícula de spin $1/2$ que compõe um conjunto completo de autoespinores com helicidade dual do operador conjugação de carga. Esses espinores recebem o nome de Elko, um acrônimo proveniente do Alemão \textit{Eigenspinoren des Ladungskonjugationsoperators}. Veremos que o elo entre os espaços de representação $(1/2, 0)$ e $(0, 1/2)$ não é dado pela simetria de paridade mas sim pela 'Mágica das matrizes de Pauli', e, portanto, como consequência a dinâmica de tais campos será regida única e exclusivamente pela dinâmica de Klein-Gordon. Tal fato faz com que o propagador associado ao Elko guarde muita similaridade com o propagador do campo escalar. Intrinsicamente, em sua formulação embrionária, as somas de spin para o Elko mostram um termo que quebra explicitamente a covariância relativística, levando então à apreciação da \textit{Very Special Relativity}, que nada mais é do que um subgrupo do grupo de Lorentz, cuja álgebra deixa as somas de spin invariantes ou covariantes. Entretanto, mostraremos que existe uma liberdade na definição da estrutura dual, a qual permite que seja construída uma teoria local e invariante p... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The present thesis covers in details a systematic study of a quantum theory based on mass dimension one fermions which satisfy the Fermi-Dirac statistics, essentially addressing its construction, field quantization, analysis of physical observables and quantum applications. We provide all the details of an unexpected theoretical discovery of a spin 1/2 particle which composes a complete set of dual helicity spinors of the charge conjugation operator. Such spinors are called Elko, an acronym for the German word Eigenspinoren des Ladungskonjugationsoperators. We show that the relation between the representation spaces (1/2,0) and (0,1/2) is given by the "Magic of Pauli matrices" rather than parity symmetry, therefore, as a consequence the dynamic of such fields is governed solely and exclusively by the Klein-Gordon dynamic. Such fact makes the Elko propagator to be very similar to the scalar field propagator Intrinsically, in its embryonic formulation, Elko spin sums shows up a term that explicitly breaks relativistic covariance, leading to the appreciation of Very Special Relativity, a theory which is based on a subgroup of the Lorentz group, whose algebra leaves the spin sums invariant or covariant. However, we show a freedom in the dual structure definition, which allows the construction of a local and Lorentz invariant theory, thus, leading to a very interesting and promising new physics / Doutor

Depuis 1916, l'étude des Trous Noirs a soulevé des questions intrigantes. Seulement certaines ont été résolues. En effet, nous faisons face à des régimes où s’entremêlent la théorie quantique et l'espace-temps. Les TN comme porte d'entrée pour comprendre la nature quantique de la gravité. Ma thèse a été entièrement dédiée à ce domaine central de la physique théorique, avec pour but la compréhension la plus large possible des débats autour de ces questions. C'est ainsi qu'ont été produits des résultats originaux qui constituent le cœur de ce manuscrit. 1-Les surfaces de volume maximal des TN sont étudiées. Un TN astrophysique terminera sa vie avec une aire planckienne de $10^{-70} m^2$ dissimulant $10^5$ fois le volume de l'univers observable. Ceci peut avoir des conséquences sur la viabilité du "remnant scenario" comme solution au paradoxe de l'information. 2-Le scénario "trou-noir-trou-blanc" est fortement instable. Une modification minimale est proposée pour résoudre ce problème. 3-Une généralisation des quatre lois de la thermodynamique des TN est démontrée pour des cônes de lumière s'intersectant dans un espace de Minkowski. 4-On étudie des espaces conformellement plats où de telles lois acquièrent une interprétation thermodynamique standard. Le plus simple est l'espace-temps de Bertotti-Robinson, connu pour encoder la géométrie proche de l'horizon d'un TN chargé. 5-Pour peu que le bon tenseur énergie-impulsion soit identifié, les équations du champ Einstein-Cartan peuvent être retrouvées comme l'équation d'état d'un équilibre thermodynamique, comme dans le cas original de la RG. Ces résultats contribuent au débat intense sur les questions cruciales posées ci-dessus. / Since 1916 intriguing questions have arisen from the study of Black Holes (BH). Only some of them have been resolved. Indeed, we are faced with regimes where the yet unknown interplay between quantum theory and spacetime unveils. BH physics is a gateway to the quantum nature of gravity. My thesis has been completely devoted to this central domain of theoretical physics, with the guiding aim of understanding in the widest possible manner the debate around those questions. The process has produced original results that constitute the main core of the manuscript. 1- The maximal volume surfaces of evaporating BHs are studied. An astrophysical BH will end its life with an external planckian area $10^{-70} m^2$ hiding $10^5$ times the volume of our observable Universe. This can have consequences on the viability of the “remnant scenario” as solution to the BH information paradox. 2- The “black-hole-to-white-hole scenario” is analyzed. The model is shown to be strongly unstable, and a minimal resolutive modification is proposed. 3- A generalisation of the four laws of BH thermodynamics is proven for intersecting light cones in Minkowski spacetime. 4- Conformally flat spaces where such laws acquire the standard thermodynamical interpretation are studied. The simplest one is the Bertotti-Robinson spacetime, known to encode the near-horizon geometry of a charged BH. 5- It is shown that, if the correct energy-momentum tensor is identified, the Eintein-Cartan’s field equations can be recovered as a thermodynamical equilibrium equation of state just like in the GR original case. Such results contribute to the intense debate on the opening crucial questions.

Um dos problemas mais importantes que precisa ser resolvido, tanto pela física de partículas como pela cosmologia, é a existência de assimetria bariônica. Entre os cenários mais atrativos para a geração dinâmica da assimetria bariônica (Bariogênese) encontra- se a denominada Leptogênese. Nesse cenário, cria-se uma assimetria leptônica que será convertida em assimetria bariônica por processos não perturbativos mediados por sphalerons. Na realização mais simples da Leptogênese, que será estudada nesta dissertação, neutrinos pesados de mão direita, produzidos termicamente, decaem violando CP, gerando um assimetria leptônica nesses decaimentos. O principal atrativo deste cenário é que conecta duas escalas aparentemente diferentes: a escala da geração de assimetria leptônica e a escala das massas e oscilações dos neutrinos ativos mediante o mecanismo de See-Saw. O estudo usual da Leptogênese utiliza equações de Boltzmann para determinar a evolução temporal da assimetria. Porém, a equação de Boltzmann é uma equação semiclássica, dado que envolve, por um lado, uma função clássica no espaço de fases, a função de distribuição, mas, por outro, os termos de colisão envolvem quantidades obtidas na teoria quântica de campos à temperatura nula. Em particular, a formulação de Boltzmann não permite descrever fenômenos quânticos como oscilações coerentes e efeitos de decoêrencia e interferência. Uma descrição quântica completa da evolução da assimetria leptônica na leptogênese deve, de fato, ser obtida no contexto da teoria quântica de campos fora do equilíbrio térmico. O formalismo de Schwinger-Keldysh permite realizar isso. Nesta dissertação descreveremos a leptogênese no formalismo de Schwinger-Keldysh para o caso em que são adicionados ao espectro de partículas do Modelo Padrão três neutrinos de mão direita, sem fazer qualquer suposição sobre a hierarquia de massas. / One of the most important problems that is needed to solve by the Elementary Particle Physics as well as by the Cosmology is the existence of baryonic asymmetry. Among the most attractive scenarios of dynamic generation of baryonic asymmetry (Baryogenesis) is the so-called Leptogenesis. In that scenario, a leptonic asymmetry is treated in such a way that it will be converted in baryonic asymmetry by non-perturbative processes mediated by sphalerons. In the simplest realization of Leptogenesis, that will be studied in this disertation, heavy right-handed neutrinos, produzed thermally, decay violating CP generating a leptonic asymmetry in these decays. The principal attractive of this scenario is that it connects two apparently different scales, the scale of leptonic asymmetry generation and the scale of masses and oscillations of the active neutrinos through the See-Saw mechanism. The usual study of the leptogenesis uses Boltzmann equations in order to determine the temporal evolution of the asymmetry. However, the Boltzmann equation is a semiclassical equations, since, on one side, it is formulated for a classical function in phases space, the distribution function, but, on the other hand, the collision term involves quantities obtained in the Quantum Field Theory at zero temperature. In particular, Boltzmann formulation does not allow to describe quantum phenomena such coherent oscillations and effects of decoherence and interference. Indeed, a proper quantum description of the evolution of the leptonic asymmetry must be obtained in the context of the Non-Equilibrium Quantum Field Theory. The Schwinger-Keldysh formalism allows to perform this. In this dissertation, leptogenesis is described using the Schwinger-Keldysh formalism for the case in which there are three right-handed neutrinos without a definite mass hierarchy.

Nesta tese estudamos o modelo CP^(N-1) em (2+1) dimensões do espaco-tempo, onde o campo básico está na representacão fundamental. Diferentemente do caso em que o campo básico está na representacão adjunta, já estudado na literatura, o modelo por nós estudado se reduz ao modelo supersimétrico usual no limite comutativo. Analisamos a estrutura de fase e calculamos as correcões dominantes e subdominantes na expansão 1/N. Provamos que a teoria é livre de singularidades infravermelhas não integráveis e é renormalizável na ordem dominante. A funcão de vértice de dois pontos do campo básico é calculada e renormalizada de uma forma explicitamente supersimétrica na ordem subdominante. / In this thesis we sutudy the noncommutative supersymmetric CP^(N-1) model in (2+1) space-time dimensions, where the basic field is in the fundamental representation which, differently to the adjoint representation already studied in the literature, goes to the usual supersymmetric model in the commutative limit. We analyse the phase structure of the model and calculate the leading and subleading corrections in the 1/N expansion. We prove that the theory is free of non-integrable IR/UV infrared singularities and is renormalizable in the leading order. The two point vertex function of the basic field is also calculated and renormalized in an expliciitly supersymmetic way up to subleading order.

O Modelo Padrão (MP) da física de partículas fornece uma descrição extremamente bem sucedida de todos os dados experimentais atuais. No entanto, temos razões para esperar que ele não seja válido até escalas de energia arbitrariamente altas. No MP a massa do bóson de Higgs é quadraticamente sensível a correções radiativas, sofrendo de grandes problemas de ajuste fino. Isso gera o chamado problema da hierarquia de gauge, cuja solução natural requer nova física na escala TeV. O MP também não fornece nenhuma explicação para a grande hierarquia de massas e ângulos de mistura dos férmions. Os problemas de hierarquia podem ser resolvidos naturalmente em teorias com uma dimensão extra curva. No entanto, a sua versão mais simples viola sabor a nível árvore, em conflito com os dados. Nesta tese investigaremos modelos quadridimensionais que descrevem a física na escala TeV obtidos da discretização de teorias em cinco dimensões no espaço AdS5, segundo o procedimento de desconstrução dimensional. As hierarquias de gauge e das massas dos férmions são geradas naturalmente como no modelo extra-dimensional, satisfazendo ainda os vínculos de sabor e de precisão eletrofraca. Estudaremos também um modelo desconstruído em que o Higgs é um pseudo bóson de Nambu-Goldstone, a fim de obter um Higgs naturalmente leve e dinamicamente localizado / The Standard Model (SM) of particle physics provides an extremely successful description of all current experimental data. However, we have reasons to expect that it cannot be valid up to arbitrarily high energy scales. In the SM the Higgs boson mass is quadratically sensitive to radiative corrections and, hence, suffers from a severe fine-tunning problem. This creates the so-called gauge hierarchy problem, the natural solution of which requires new physics at the TeV scale. The SM also doesnt provide any explanation for the large hierarchy of fermion masses and mixing angles. The hierarchy problems can be naturally solved in theories with a warped extra dimension. However, their simplest version violates flavor at tree level, conflicting with experimental data. In this thesis we investigate four dimensional models that describe physics at the TeV scale obtained from a coarse discretization of five dimensional theories in AdS5 space, by the dimensional deconstruction procedure. The gauge as well as the fermion mass hierarchies are naturally generated in the same manner as in the extra-dimensional model, while also satisfying bonds from flavor physics and precision electroweak data. We also study a deconstructed model in which the Higgs is a pseudo Nambu-Goldstone boson, with the motivation of obtaining a naturally light and localized Higgs.

In dieser Arbeit wird eine systematische Methode gegeben um die Amplituden in (skalarer) Quantenelektrodynamik und nicht-Abelsche Eichtheorien in Schwinger-parametrische Form zu schreiben. Dies wird erreicht in dem der Zähler der Feynmanregeln im Impulsraum in einem Differentialoperator umgewandelt wird. Dieser Differentialoperator wirkt dann auf den parametrichen Integranden der skalaren Theorie. Für die QED ist das am einfachsten, weil die Leibnizregel hier nicht nötig ist. Im Fall der sQED und den nicht-Abelsche Eichtheorien stehen die Beiträge der Leibnizregel in Verbindung mit 4-valente Vertices. Eine andere Eigenschaft dieser Methode ist, dass mit dem hier benutzten Renormierungsschema die Subtraktionen für 1-scale Graphen signifikante Vereinfachungen verursachen. Weiterhin wurden die Ward-Identitäte für die genannten drei Theorien studiert. / In this thesis a systematic method is given for writing the amplitudes in (scalar) quantum electrodynamics and non-Abelian gauge theories in Schwinger parametric form. This is done by turning the numerator of the Feynman rules in momentum space into a differential operator. It acts then on the parametric integrand of the scalar theory. For QED it is the most straightforward, because the Leibniz rule is not involved here. In the case of sQED and non-Abelian gauge theories, the contributions from the Leibniz rule are satisfyingly related to 4-valent vertices. Another feature of this method is that in the used renormalization scheme, the subtractions for 1-scale graphs cause significant simplifications. Furthermore, the Ward identities for mentioned three theories are studied.

Diese Arbeit befasst sich mit Quantenfeldtheorien auf nicht-kommutativen Räumen. Solche Modelle treten im Zusammenhang mit der Stringtheorie und mit der Quantengravitation auf. Ihre nicht-störungstheoretische Behandlung ist üblicherweise schwierig. Hier untersuchen wir jedoch drei nicht-kommutative Quantenfeldtheorien nicht-perturbativ, indem wir die Wirkungsfunktionale in eine äquivalente Matrixformulierung übersetzen. In der Matrixdarstellung kann die jeweilige Theorie dann numerisch behandelt werden. Als erstes betrachten wir ein regularisiertes skalares Modell auf der nicht-kommutativen Ebene und untersuchen den Kontinuumslimes bei festgehaltener Nicht-Kommutativität. Dies wird auch als Doppelskalierungslimes bezeichnet. Insbesondere untersuchen wir das Verhalten der gestreiften Phase. Wir finden keinerlei Hinweise auf die Existenz dieser Phase im Doppelskalierungslimes. Im Anschluss daran betrachten wir eine vier-dimensionale U(1) Eichtheorie. Hierbei sind zwei der räumlichen Richtungen nicht-kommutativ. Wir untersuchen sowohl die Phasenstruktur als auch den Doppelskalierungslimes. Es stellt sich heraus, dass neben den Phasen starker und schwacher Kopplung eine weitere Phase existiert, die gebrochene Phase. Dann bestätigen wir die Existenz eines endlichen Doppelskalierungslimes, und damit die Renormierbarkeit der Theorie. Weiterhin untersuchen wir die Dispersionsrelation des Photons. In der Phase mit schwacher Kopplung stimmen unsere Ergebnisse mit störungstheoretischen Berechnungen überein, die eine Infrarot-Instabilität vorhersagen. Andererseits finden wir in der gebrochenen Phase die Dispersionsrelation, die einem masselosen Teilchen entspricht. Als dritte Theorie betrachten wir ein einfaches, in seiner Kontinuumsform supersymmetrisches Modell, welches auf der "Fuzzy Sphere" formuliert wird. Hier wechselwirken neutrale skalare Bosonen mit Majorana-Fermionen. Wir untersuchen die Phasenstruktur dieses Modells, wobei wir drei unterschiedliche Phasen finden. / This work deals with three quantum field theories on spaces with noncommuting position operators. Noncommutative models occur in the study of string theories and quantum gravity. They usually elude treatment beyond the perturbative level. Due to the technique of dimensional reduction, however, we are able to investigate these theories nonperturbatively. This entails translating the action functionals into a matrix language, which is suitable for numerical simulations. First we explore a scalar model on a noncommutative plane. We investigate the continuum limit at fixed noncommutativity, which is known as the double scaling limit. Here we focus especially on the fate of the striped phase, a phase peculiar to the noncommutative version of the regularized scalar model. We find no evidence for its existence in the double scaling limit. Next we examine the U(1) gauge theory on a four-dimensional spacetime, where two spatial directions are noncommutative. We examine the phase structure and find a new phase with a spontaneously broken translation symmetry. In addition we demonstrate the existence of a finite double scaling limit which confirms the renormalizability of the theory. Furthermore we investigate the dispersion relation of the photon. In the weak coupling phase our results are consistent with an infrared instability predicted by perturbation theory. If the translational symmetry is broken, however, we find a dispersion relation corresponding to a massless particle. Finally, we investigate a supersymmetric theory on the fuzzy sphere, which features scalar neutral bosons and Majorana fermions. The supersymmetry is exact in the limit of infinitely large matrices. We investigate the phase structure of the model and find three distinct phases. Summarizing, we study noncommutative field theories beyond perturbation theory. Moreover, we simulate a supersymmetric theory on the fuzzy sphere, which might provide an alternative to attempted lattice formulations.