Orientador: Maria Cristina Batoni Abdalla / Co-orientador: Ion Vasile Vancea / Banca: José Abdalla Helaÿel Neto / Banca: Ademir Eugenio de Santana / Banca: Jeferson de Lima Tomazelli / Banca: Bruto Max Pimentel Escobar / Resumo: Apresentamos uma formulação geral para a Dinâmica de Campos Térmicos em termos de geradores que satisfazem a álgebra do grupo SU(1,1). Introduzimos o Operador Entropia dentro deste contexto. Construímos estados de contorno bosônicos à temperatura finita. Estes estados são interpretados como Dp-branas térmicas. A entropia da corda bosônica fechada, bem como a da Dp-brana térmica na presença de um campo externo abeliano constante, é obtida / Abstract: A general formulation of Thermo Field Dynamics using su(1,1) generators is presented. In this framework an entropy operator is introduced and boundary state is constructed at finite temperature. This boundary state is interpreted as a thermal Dp-brane. The entropy of bosonic closed string is obtained as well that of Dp-brane in an abelian external field using the general expression for the entropy operator / Doutor

Orientador: Antonio José Accioly / Banca: Ion Vasile Vancea / Banca: Maria Emilia Xavier Guimarães / Banca: Sérgio José Barbosa Duarte / Banca: Sebastião Alves Dias / Resumo: A generalização da gravitação em 2+1 dimensões através da inclusão de termos de ordem superior dá origem a uma série de questões interessantes. O mesmo não ocorre na gravitação de Einstein, que é uma teoria covariante sem graus de liberdade dinâmicos - uma peculiaridade, aliás, que a torna insípida e inodora. O estudo das propriedades de uma partícula movendo-se em um plano, no contexto da gravitação de ordem superior, origina alguns efeitos novos e interessantes como, por exemplo, a geração de três regimes de interação - gravitação, antigravitação e blindagem gravitacional - entre dois bósons massivos pela troca de um gráviton. Além do mais, o ângulo de deflexão do fóton, ao contrário da teoria de Einstein, depende do parâmetro de impacto. Por outro lado, a grande desvantagem em usar a versão linearizada da teoria de Einstein para descrever a gravidade ao redor de uma corda cósmica é que ela leva a alguns efeitos indesejáveis, como por exemplo: (I) ausência de força gravitacional no limite não relativístico; (ii) deflexão gravitacional independente do parâmetro de impacto. Supreendentemente, a cura para esses males é obtida pela substituição da gravitação linearizada por sua correspondente versão de ordem superior. Essas questões serão tratadas aqui / Abstract: The possibility of generalizing gravity in 2+1 dimensions to include higher-derivative terms, thereby allowing for a dynamical theory, opens up a variety of new interesting questions. This is in great contrast with pure Einstein gravity which is a generally covariant theory that has no degrees of freedom - a peculiarity that, in a sense, renders it a little insipid and odorless. The research on gravity of particles moving in a plane, that is, living in flatland, within the context of higher-derivative gravity, leads to novel and interesting effects. For instance, the generation of gravity, antigravity, and gravitational shielding by the interaction of massive scalar bosons via a graviton exchange. In addition, the gravitational deffection angle of a photon, unlike that of Einstein gravity, is dependent of the impact parameter. On the other hand, the great drawback to using linearized general relativity for describing a gravitating string is that this description leads to some unphysical results such as: (i) lack of a gravity force in the nonrelativistic limit; (ii) gravitational deffection independent of the impact parameter. Interesting enough, the effective cure for these pathologies is the replacement of linearized gravity by linearized higher-derivative gravity. We address these issues here / Doutor

Orientador: Abraham Hirsz Zimerman / Banca: Clisthenis Ponce Constantinidis / Banca: Harold Socrates Blas Achic / Banca: Andrei Mikhailov / Banca: Marcio José Martins / Resumo: Nesta tese discutimos as propriedades de integrabilidade das teorias de campo clássicas em duas dimensões na presença de descontinuidades ou defeitos tipo-II, principalmente usando a linguagem do formalismo do espalhamento inverso. Um método geral para calcular a função geradora de um conjunto infinito de grandezas conservadas modificadas para qualquer equação de campo integrável é apresentado, uma vez que seus respetivos problemas lineares associados são dados e suas correspondentes matrices do defeito são calculadas. O método é aplicado no cálculo das contribuições dos defeitos para a energia e o momento para vários modelos e mostramos a relação entre as condições de defeito integráveis e suas respevtivas transformações de Bäcklund para cada modelo / Abstract: In this thesis we discuss the integrability properties of two-dimensional classical field theories in the presence of discontinuities or type-II defects, mainly using the language of the inverses cattering approach. We present a general method to compute the generating function of an infinite set of modified conserved quantities for any integrable field equation givent heir associated linear problems and computing their corresponding defect matrices. We apply this method to derive in particular defect contributions to the energy and momentum for several models and show the relationship between the integrable defect conditions and the Bäcklund transformations for each model / Doutor

Orientador: Bruto Max Pimentel Escobar / Banca: Julio Marny Hoff da Silva / Banca: Fabrício Augusto Barone Rangel / Banca: Abraham Hirsz Zimerman / Banca: Fernando Tadeu Caldeira Brandt / Resumo: Este trabalho tem como objetivo explorar a dinâmica quântica de interação entre partículas escalares e vetoriais e estudar o equilíbrio termodinâmico dessas partículas no ensemble gran-canônico. A dinâmica de interação, escrita em uma linguagem covariante entre o campo de matéria (escalar) e o campo intermediador de interação (vetorial), apresenta uma simetria de calibre local, U(1) no caso quântico e SO(4) no equilíbrio termodinâmico. Sendo assim dividimos o trabalho em dois setores. No primeiro setor analisamos sistematicamente a interação quântica entre partículas escalares (mésons) e partículas vetoriais (fótons) no contexto da eletrodinâmica quântica escalar generalizada de Duffin-Kemmer-Petiau (GSDKP). Para isso quantizamos a teoria, utilizando uma abordagem funcional. Construímos a estrutura Hamiltoniana do sistema seguindo a metodologia de Dirac, o procedimento de Faddeev-Senjanovic para obter a amplitude de transição no calibre de Coulomb generalizado e o método de Faddeev-Popov-DeWitt para escrever a amplitude de transição anterior de maneira covariante na condição de calibre no-mixing. Daí, escrevendo o funcional gerador via Schwinger, as equações de Schwinger-Dyson (SD) e as identidades de Ward-Takahashi (WT) são obtidas. Como introdução à análise das correções radiativas, fizemos um cálculo quantitativo para ver os tipos de divergências superficiais (ultravioleta) que poderiam aparecer na teoria. Depois apresentamos um cálculo explícito das primeiras correções radiativas (1-laço) associadas ao propagador do fóton, propagador do méson, vértice e, estudamos a função de 4 pontos (fóton-fóton) utilizando o método de regularização dimensional, em que a simetria de calibre é manifesta. Como veremos, uma consequência do estudo é que a álgebra de DKP assegura o funcionamento das identidades de WT nas primeiras correções radiativas... / Abstract: This work has as aim to explore the quantum dynamics of interaction between scalar and vectorial particles and to study the thermodynamic equilibrium of these particles in the gran-canonical ensemble. The dynamics of interaction, written in a covariance language, between the matter field (scalar) and the field that intermediate the interaction (vectorial) exhibit a local gauge symmetry, U(1) in a quantum case and SO(4) in a thermodynamic equilibrium. Therefore we divided the work into two sections. In the first section we analyze systematically the quantum interaction between the scalar particles (mesons) and vectorial particles (photons) in the context of the generalized scalar Duffin-Kemmer-Petiau quantum electrodynamics (GSDKP). For this we use the functional approach to quantize the theory. We built the hamiltonian structure by the Dirac methodology, utilize the Faddeev-Senjanovic procedure to obtain the transition amplitude in the generalized Coulomb gauge and the Faadeev-Popov-DeWitt method to write the covariant form of the previously amplitude in the no-mixing gauge condition. Then writing the functional generator by Schwinger, the Schwinger-Dyson (SD) equations and the Ward-Takahashi (WT) identities are obtained. As an introductory analysis to the first radiative corrections we make a quantitative calculus to see the types of ultraviolet (UV) superficial divergences that appear in the theory. After this we show an explicit calculation of the first radiative corrections (1-loop) associated with the photon propagator, meson propagator, vertex and the 4 point function (photon-photon) utilizing the dimensional regularization method, where the gauge symmetry is manifest. As we will see one of the consequences of the study is that the DKP algebra ensures the functioning of the WT identities in the first radiative corrections prohibiting certain UV divergences. With the knowledge of the UV divergen... / Doutor

In this work, we develop effective field theory (EFT) methods for the study of a wide variety of condensed matter systems, including superfluids, ordinary fluids, solids, and supersolids. As a first application, we focus on the dynamics of vortex lines in trapped superfluid condensates, studying their precessional motion and working out the frequency of precession from EFT principles. We consider the effects of trapping in two and three dimensions, as well as implications of trapping for the dispersion relation of Kelvin waves along superfluid vortex lines. We also apply our formalism to study the effects of gravitational fields on sound waves in several different media, discovering that localized sound waves propagate with an associated (negative) net mass, which in turn generates a tiny gravitational field. We confirm that this effect is a robust result that can be found from purely classical, non-relativistic methods. We then present three Lorentz invariant, renormalizable, weakly coupled theories that implement the symmetry-breaking pattern of a perturbative homogeneous and isotropic solid, as potential UV-completions of the low-energy effective theory that we studied. We demonstrate that a particular class of homogeneous, isotropic solids at long distances corresponds to states that are also homogeneous at short distances, unlike typical solids found in nature. We find that each case leads to the same rather unorthodox effective theory of a solid with luminal transverse excitations. Finally, we discuss applications of the methods we have developed and the potential for interesting new directions of this research.

In this work, we develop an effective field theory program for many-body systems out of finite temperature equilibrium. Building on recent work, we combine powerful mathematical tools such as the Schwinger-Keldysh closed-time-path formalism, the coset construction, and Wilsonian effective field theory to construct novel actions that describe a wide range of many-body systems out of finite-temperature equilibrium. Unlike ordinary actions, these non-equilibrium actions account for dissipation and statistical and quantum fluctuations. The novel actions constructed include those for solids, supersolids, nematic liquid crystals, smectic liquid crystals in phases A, B, and C, chemically reacting fluids, quasicrystals, higher-form dual theories of superfluids and solids, and plasmas that can support large charge density. In order to construct these actions, we propose a new kind of coset construction with a total of four distinct types of inverse Higgs constraints. We extend the coset construction to account for higher-form symmetries and investigate the relationship between two kinds of ’t Hooft anomalies and spontaneous symmetry breaking.

research submitted to the Faculty of Science, University of the Witwatersrand, in ful llment for the degree of Master of Science in Physics / Supersymmetry plays a main role in all current thinking about superstring theory. Indeed, many remarkable properties of string theory have been explained using supersymmetry as a tool. In this dissertation, we review the basics formulation of supersymmetric quantum mechanics starting with introducing the concepts of supercharges and superalgebra. We show that, if there is a supersymmetric state, it is the zero-energy ground state. If such a state exists, the supersymmetry is unbroken otherwise it is broken. So far, there has been no unbroken supersymmetry observed in nature, and if nature is described by supersymmetry, it must be broken. In fact, supersymmetry may be broken spontaneously at any order of perturbation theory, or dynamically due to non-perturbative e ects. The goal of this dissertation is to study the methods of supersymmetry breaking. For this purpose, a special attention is given to discuss the normalization of the ground state of the supersymmetric harmonic oscillator. Then we explain that perturbation theory gives us incorrect results for both the ground state wave function as well as the energy spectrum and it fails to give an explanation to the supersymmetry breaking. Later in the dissertation, a review of the uses of instantons in quantum mechanics is given. In particular, instantons are used to compute the tunneling e ects within the path integral approach to quantum mechanics. As a result, we give evidence that the instantons, which are a non-perturbative e ect in quantum mechanics and can not be seen in perturbation theory, leads to calculate the corrections to the ground state energy and provides a possible explanation for the supersymmetry breaking. / E.K. 2019

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. Johannesburg, 2016. / The AdS/CFT correspondence is a conjectured exact duality between type IIB string theory on the AdS5 S5 background and N = 4 Super Yang-Mills theory, a conformal eld theory (CFT), on the boundary of the AdS space. A speci c observable of the CFT, which can be read from the two point correlation function, is the anomalous dimension. In this dissertation we will compute spectra of anomalous dimensions of excited giant gravitons up to two loops in a speci c limit. We are interested in the anomalous dimensions because the AdS/CFT correspondence associates them with energies of states in quantum gravity. We study operators constructed using n Z elds and m Y elds with n << m: In this case m n is a small parameter. At the leading order in m n and at large N, the problem of determining the anomalous dimensions can be mapped into the dynamics of m non-interacting magnons. The subleading terms at two loops, computed for the rst time in this dissertation, induce interactions between the magnons. Even after including this new correction, we nd the BPS operators remain BPS. / MT2016

Orientador: Denis Dalmazi / Banca: Álvaro de Souza Dutra / Banca: Elias Leite Mendonça / Banca: Bruto Max Pimentel Escobar / Banca: Victor de Oliveira Rivelles / Resumo: Partículas massivas de spin-2 são usualmente descritas pela conhecida teoria de Fierz-Pauli através de um tensor de rank-2 simétrico hµν = hνµ. Recentemente, tem havido um aumento no interesse por teorias que descrevam esse tipo de partícula, principalmente pela possibilidade de oferecer uma explicação alternativa para o problema da aceleração da expansão do universo, pois se o gráviton tivesse uma pequena massa, a força gravitacional diminuiria a grandes distâncias, produzindo tal aceleração. Trabalhos mais recentes têm trazido à tona outras possibilidades além de Fierz-Pauli para se descrever partículas de spin-2 massivas partindo de um tensor de rank-2 não simétrico eµν 6= eνµ, os chamados modelos L(a1). Tendo em vista que toda partícula deve interagir com a gravitação, no presente trabalho buscamos estudar o acoplamento desses novos modelos com um campo gravitacional de fundo. Para isso, a partir da manipulação das equações de movimento, procuramos obter os vínculos necessários para se ter uma teoria com a contagem de graus de liberdade correta. Fizemos também um estudo preliminar da versão sem massa dos modelos L(a1) no espaço curvo a partir da análise das simetrias de gauge existentes. Identificamos ainda os modelos parcialmente simétricos presentes em L(a1) / Abstract: Massive spin-2 particles are usually described by the well-known Fierz-Pauli theory via a symmetric rank-2 tensor hµν = hνµ. Recently there has been an increase of interest in theories describing this kind of particle, especially because they can contribute to explain the accelerated expansion of the universe, since if the graviton has a small mass, the gravitational force would decrease at large distances, producing such accelerattion. In recent works other possibilities, besides the Fierz-Pauli model, which describe massive spin-2 particles starting from a non-symmetric rank-2 tensor eµν 6= eνµ have been found, the so-called L(a1) models. Since every particle has to interact with the gravitation, we have studied the coupling of the new models with a background gravitational field. Therefore, from the manipulation of the equations of motion, we seek for the necessary constraints in order to achieve the correct counting of degrees of freedom. We also have done a preliminary study of the massless version of the L(a1) models in the curved space from the analysis of the gauge symmetries of the theory. We also have identified the partially symmetric models present in L(a1). / Doutor

Made available in DSpace on 2017-03-14T14:10:11Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-10-30. Added 1 bitstream(s) on 2017-03-14T14:42:52Z : No. of bitstreams: 1 000878238.pdf: 606557 bytes, checksum: be8f72226bb5bb73cf911f0b1eb0aff8 (MD5) / Dados experimentais de supernovas tem indicado uma expansão acelerada do Universo a grandes distancias. Isso tem motivado a formulação de teorias de gravidade massiva, pois com um gráviton massivo poderíamos modificar a gravidade no infravermelho, sem a necessidade de introduzir uma energia escura. Grande parte das teorias de gravidade massiva reduzem-se a n'nível linear ao modelo de Fierz-Pauli, que 'e de segunda ordem em derivadas e descreve partículas massivas de spin 2. Então, 'e natural indagarmos se há possíveis modelos alternativos duais ao modelo de Fierz-Pauli. Neste trabalho obtemos descrições alternativas para partículas massivas de spin 2. Mostramos que em D ≥ 3 há duas famílias de modelos de segunda ordem que descrevem partículas massivas de spin 2 através de um tensor não simétrico de rank 2. Obtivemos também descrições alternativas de partículas massivas de spin 2 através do procedimento de imersão do tensor de Euler de Fierz-Pauli. Todos os modelos obtidos são livres de fantasmas a n'nível quadrático, embora a maioria deles seja de ordem superior em derivadas. Os modelos que obtivemos podem ser escritos numa versão não linear em termos de uma m'métrica dinâmica e uma m'métrica fixa. Na parte final deste trabalho apresentamos duas versões não lineares de um modelo que descreve partículas de spin 2 massivas, porém com simetria de gauge, generalizando o modelo BF topologicamente massivo, que descreve partículas massivas de spin 1. Uma delas corresponde a um modelo biométrico com um novo acoplamento derivativo entre as métricas / Experimental data of supernova have indicated an accelerated expansion of the Universe at large distances. This has motivated the formulation of massive gravity theories, since a tiny mass for the graviton would certainly diminish the gravitational interaction at large distances without the need to introduce the dark energy. Much of the theories built for massive gravity reduce to the Fierz-Pauli model at linearized level, which is second order (in derivatives) and describes massive spin-2 particles. So it is natural to ask for possible alternative dual models to the Fierz-Pauli model. In this work we obtain alternative descriptions of massive spin-2 particles. We show that in arbitrary dimensions D ≥ 3 there are two families of linearized second order Lagrangians describing massive spin- 2 particles via a non-symmetric rank-2 tensor. We have also obtained alternative descriptions of massive spin-2 particles by an embedding procedure of the Fierz-Pauli equations of motion. All models are free of ghosts at the quadratic level, although most of them are of a higher order in derivatives. The models that we obtain can be nonlinearly completed in terms of a dynamic and a fixed metric. In the final part of this work we present two nonlinear versions of a linear model describing massive spin-2 particles, but with gauge symmetry, generalizing the topologically massive BF model, which describes massive spin-1 particles. One of the models corresponds to a bimetric model with a new derivative coupling between the metrics