Let M = H³/Γ be a complete, non-compact, oriented geometrically finite hyperbolic 3-manifold without cusps. By constructing a conformal compactification of M x S¹ we functorially associate to M an oriented, conformally flat, compact 4-manifold X (without boundary) with an S¹-action. X determines M as a hyperbolic manifold. Using our functor and the differential geometry of conformally flat 4-manifolds we prove that any Γ as above with a limit set of Hausdorff dimension ≤ 1 is Schottky, Fuchsian or extended Fuchsian. Furthermore, the Hodge theory for H² (X;R) carries over to H¹(M, δM;R) and H²(M;R) which correspond to the spaces of harmonic L²-forms of degree 1 and 2 on M. Comparison of lattices through the Hodge star gives an invariant h(M) ε GL(H²(M;R)/GL(H²(M;Z)) of the hyperbolic structure. Secondly we pay attention to magnetic monopoles on M which correspond to S¹invariant solutions of the anti-self-duality equations on X. The basic result is that we associate to M an infinite collection of moduli spaces of monopoles , labelled by boundary conditions. We prove that the moduli spaces are not empty (under reasonable conditions), compute their dimension , prove orientability , the existence of a compactification and smoothness for generic S¹-invariant conformal structures on X. For these results one doesn't need a hyperbolic structure on M , the existence of a conformal compactification X suffices. A twistor description for monopoles on a hyperbolic M can be given through the twistor space of X , and monopoles turn out to correspond to invariant holomorphic bundles on twistor space. We analyse these bundles. Explicit formulas for monopoles can be found on handlebodies M , and for M = surface x R we describe the moduli spaces in some detail.

In 1931 P.A.M. Dirac postulated the existence of a quantum of magnetic charge, the magnetic monopole. Since its prediction, cosmic ray and accelerator experiments have been performed to detect the monopole, but all have failed. M. Ruderman and D. Zwanziger have put forward an explanation for the negative experimental results. They argue that monopoles are likely to be produced in pairs, which are tightly bound and never become free. Ruderman and Zwanziger point to certain anomalous cosmic ray events as evidence of production of bound monopole pairs. In this paper we review Dirac's arguments, calculate the monopole's properties, and critically review previous monopole experiments. Using the model proposed by Ruderman and Zwanziger to give identifying properties, we propose an experiment designed to detect the materialization of the magnetic monopole. / Master of Science

In this thesis, we study the subject of geometrical phases in detail by considering its various forms. We focus primarily on the relation between quantum geometrical phases and magnetic monopoles, and study how one can make use of the concepts of geometrical phases to define magnetic monopoles.

The physical world is, for the most part, modelled using second order ordinary differential equations. The time-dependent simple harmonic oscillator and the Ermakov-Pinney equation (which together form an Ermakov system) are two examples that jointly and separately describe many physical situations. We study Ermakov systems from the point of view of the algebraic properties of differential equations. The idea of generalised Ermakov systems is introduced and their relationship to the Lie algebra sl(2, R) is explained. We show that the 'compact' form of generalized Ermakov systems has an infinite dimensional Lie algebra. Such algebras are usually associated only with first order equations in the context of ordinary differential equations. Apart from the Ermakov invariant which shares the infinite-dimensional algebra of the 'compact' equation, the other three integrals force the dimension of the algebra to be reduced to the three of sl(2, R). Subsequently we establish a new class of Ermakov systems by considering equations invariant under sl(2, R) (in two dimensions) and sl(2, R) EB so(3) (in three dimensions). The former class contains the generalized Ermakov system as a special case in which the force is velocity-independent. The latter case is a generalization of the classical equation of motion of the magnetic monopole which is well known to possess the conserved Poincare vector. We demonstrate that in fact there are three such vectors for all equations of this type. / Thesis (M.Sc.)-University of Natal, 1993.

Ανασκόπηση τηε θεωρίας Dirac σχετικά με τα μαγνητικά μονόπολα και αποτελέσματα της. Ανασκόπηση εννοιών από την τοπολογία και την διαφορική γεωμετρία, με την βοήθεια των οποίων, περιγράφουμε την θεωρία των t'Hooft-Polyakov, και συγκεκριμένα την λύση που βρήκαν που αντιστοιχεί σε μαγνητικό μονόπολο στην μη αβελιανή θεωρία με ομάδα βαθμίδας την SU(2). Τέλος, εξετάζονται τα γενικά χαρακτηριστικά των μονοπολικών λύσεων με τοπολογικά επιχειρήματα και γενικεύονται τα αποτελέσματα προηγούμενων ενοτήτων. / Dirac theory of magnetic monopoles. Aspects of topology and differential geometry. The t'Hooft - Polyakov solution in non abelian gauge theory with gauge group SU(2). General properties of monopole solutions from a topological point of view.

Made available in DSpace on 2018-07-27T18:26:08Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-09-04. Added 1 bitstream(s) on 2018-07-27T18:30:19Z : No. of bitstreams: 1 000866848.pdf: 631406 bytes, checksum: 951f24cae0a92bf26987f68a9faaef16 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Nesta dissertação apresentamos uma descrição da dualidade elétrica-magnética e seus aspectos clássicos e quânticos. Nosso análise se inicia com os monopolos magéticos sugeridos por Dirac em 1931[1] e vai até o trabalho do Seiberg e Witten em 1994 [27]. Na descrição clássica, precisamos introduzir os monopolos magnéticos a fim de obter a dualidade elétrica-magnética manifesta. Mais tarde, a origem dos monopolos se mais torna mais clara quando começamos com uma teoria de Yang-Mills. Os aspectos clássicos da teoria foram explicados pela conjetura de Montonen e Olive 1977 [7]. Explorando os aspectos quânticos da teoria, notamos a importância de introduzir supersimetria, principalmente supersimetria estendida, onde tiramos vantagem da propiedade de holomorficidade, a qual nos leva aos teoremas não renormalizáveis, onde o cálculo é mais simples. Focamos na teoria de gauge supersimétrica N = 2 SU(2). A teoria é completamente resolvível para baixas energias. A maior parte do conteúdo deste trabalho é baseada nas várias revisões da dualidade de Seiberg-Witten [30],[31],[32] / In this dissertation we present a description of the electric-magnetic duality and their classical and quantum aspects. Our analysis starts from the suggested magnetic monopoles by Dirac in 1931 [1] and goes until the work of Seiberg and Witten in 1994 [27]. In the classical description, we need to introduce the magnetic monopoles in order to make manifest the electricmagnetic duality. Later, the origin of monopoles becomes clear when we start from a Yang-Mills theory. The classical aspects of the E-M duality are covered in the Montonen-Olive conjecture 1977[7]. Working on the quantum aspects of the theory, we note the importance of introducing supersymmetry. Specially for extended supersymmetry, where we take advantage of the holomorphicity property, which leads us to the non-renormalizable theorems, where the computation is easier. We focus on theN = 2SU(2) supersymmetric gauge theories. It turns out that the theory is fully solvable at the low energies regime[27]. Most of this work is based on reviews about the Seiberg and Witten duality [30],[31],[32]

Orientador: Nathan Jacob Berkovits / Banca: Horatiu Stefan Nastase / Banca: Diego Trancanelli / Resumo: Nesta dissertação apresentamos uma descrição da dualidade elétrica-magnética e seus aspectos clássicos e quânticos. Nosso análise se inicia com os monopolos magéticos sugeridos por Dirac em 1931[1] e vai até o trabalho do Seiberg e Witten em 1994 [27]. Na descrição clássica, precisamos introduzir os monopolos magnéticos a fim de obter a dualidade elétrica-magnética manifesta. Mais tarde, a origem dos monopolos se mais torna mais clara quando começamos com uma teoria de Yang-Mills. Os aspectos clássicos da teoria foram explicados pela conjetura de Montonen e Olive 1977 [7]. Explorando os aspectos quânticos da teoria, notamos a importância de introduzir supersimetria, principalmente supersimetria estendida, onde tiramos vantagem da propiedade de holomorficidade, a qual nos leva aos teoremas não renormalizáveis, onde o cálculo é mais simples. Focamos na teoria de gauge supersimétrica N = 2 SU(2). A teoria é completamente resolvível para baixas energias. A maior parte do conteúdo deste trabalho é baseada nas várias revisões da dualidade de Seiberg-Witten [30],[31],[32] / Abstract: In this dissertation we present a description of the electric-magnetic duality and their classical and quantum aspects. Our analysis starts from the suggested magnetic monopoles by Dirac in 1931 [1] and goes until the work of Seiberg and Witten in 1994 [27]. In the classical description, we need to introduce the magnetic monopoles in order to make manifest the electricmagnetic duality. Later, the origin of monopoles becomes clear when we start from a Yang-Mills theory. The classical aspects of the E-M duality are covered in the Montonen-Olive conjecture 1977[7]. Working on the quantum aspects of the theory, we note the importance of introducing supersymmetry. Specially for extended supersymmetry, where we take advantage of the holomorphicity property, which leads us to the non-renormalizable theorems, where the computation is easier. We focus on theN = 2SU(2) supersymmetric gauge theories. It turns out that the theory is fully solvable at the low energies regime[27]. Most of this work is based on reviews about the Seiberg and Witten duality [30],[31],[32] / Mestre

abstract: In this dissertation, I present the results from my recent investigations into the interactions involving topological defects, such as magnetic monopoles and strings, that may have been produced in the early universe. I performed numerical studies on the interactions of twisted monopole-antimonopole pairs in the 't Hooft-Polyakov model for a range of values of the scalar to vector mass ratio. Sphaleron solution predicted by Taubes was recovered, and I mapped out its energy and size as functions of parameters. I also looked into the production, and decay modes of $U(1)$ gauge and global strings. I demonstrated that strings can be produced upon evolution of gauge wavepackets defined within a certain region of parameter space. The numerical exploration of the decay modes of cosmic string loops led to the conclusions that string loops emit particle radiation primarily due to kink collisions, and that their decay time due to these losses is proportional to $L^p$, where $L$ is the loop length and $p \approx 2$. In contrast, the decay time due to gravitational radiation scales in proportion to $L$, and I concluded that particle emission is the primary energy loss mechanism for loops smaller than a critical length scale, while gravitational losses dominate for larger loops. In addition, I analyzed the decay of cosmic global string loops due to radiation of Goldstone bosons and massive scalar ($\chi$) particles. The length of loops I studied ranges from 200-1000 times the width of the string core. I found that the lifetime of a loop is approximately $1.4L$. The energy spectrum of Goldstone boson radiation has a $k^{-1}$ fall off, where $k$ is the wavenumber, and a sharp peak at $k\approx m_\chi/2$, where $m_\chi$ is the mass of $\chi$. The latter is a new feature and implies a peak at high energies (MeV-GeV) in the cosmological distribution of QCD axions. / Dissertation/Thesis / Doctoral Dissertation Physics 2020

Made available in DSpace on 2015-03-26T13:35:18Z (GMT). No. of bitstreams: 1 texto completo.pdf: 2056393 bytes, checksum: 6c718958e16dde37636b88ed5dbf583f (MD5) Previous issue date: 2012-02-14 / Fundação de Amparo a Pesquisa do Estado de Minas Gerais / We study the magnetic excitations in two-dimensional spin ices on square lattices, by means of computer simulations. These materials are artificially produced by lithographic techniques, using ferromegnetic nano-islands arranged in a lattice especially organized in such a way, that, the lattice geometry together with the dipole-dipole interactions lead to an intrinsic frustration of the system. Our analysis, based only on the dipolar interaction between the islands, correctly reproduces the ground state experimentally observed recently. In addition, we verify the emergence of magnetic excitations that behave like magnetic monopoles, carrying isolated magnetic charge. These quasi-particles interact by means of the Coulomb potential plus a linear confining potential, which is attributed to the emergence of string-like excitations, linking the pair of opposite charges. However, we argue that the string has a configurational entropy, so that the string tension may decrease as the temperature is increased and then, free magnetic monopoles should be found in two-dimensional spin ices at a critical temperature. We also study the case where the artificial spin ice is built with missing nano-island (vacancy). For the case with only one vacancy, we found that the defect modify the potential obtained for the normal lattice. The vacancy behaves like a pair of opposite charges, carrying half charge of the usual magnetic monopole excitation. Our calculations show that when the smallest distance between the charges (or the string) is greater than 2a (a is the lattice spacing), the interaction of the string with the defect is negligible. However, for distances smaller than 2a, the string interacts with the defect more appreciable, in a very complicated way, which depends on the shape and size of the string. Our results indicate that, on each vertex where the string passes, there is an additional quadrupole moment and so the field created by the string decays very quickly. / Nós estudamos as excitações magnéticas que surgem nos gelos de spin bidimensionais, por meio de simulações computacionais em redes quadradas. Esses materiais são produzidos artificialmente, através de técnicas litográficas utilizando nanopartículas ferromagnéticas arranjadas em uma rede especialmente organizada, de modo que a geometria da rede juntamente com a interação dipolo-dipolo leva a uma frustração intríseca do sistema. A análise, baseada somente na interação dipolar entre as nanoilhas, reproduz corretamente o estado fundamental recentemente observado experimentalmente. Foi verificado a emergência de excitações magnéticas que se comportam como monopolo magnético, carregando carga magnética isolada. Essas quasi-partículas interagem via potencial coulombiano adicionado a um potencial confinante linear, atribuído ao aparecimento de excitações do tipo corda, que conectam o par monopolo-antimonopolo. Contudo, verificamos que a corda possui uma entropia configuracional, de modo que a tensão da corda pode diminuir à medida em que a temperatura é aumentada, fazendo com que os monopolos magnéticos possam ser encontrados livres nos gelos de spin bidimensionais em uma temperatura crítica. Também estudamos o caso em que o gelo de spin é construído com uma única ilha faltante em uma dada posição da rede. Foi visto que o defeito pertuba o potencial obtido em uma rede normal. A vacância se comporta como um par de cargas opostas carregando metade da carga do monopolo magnético usual. Nossos cálculos mostram que quando a menor distância entre uma carga e a vacância é maior que 2a (a é o espaçamento de rede), a interação entre a corda e o defeito é negligenciável. Contudo, para distâncias menores que 2a, a corda interage mais apreciavelmente com o defeito, de uma forma muito complicada que depende de seu tamanho e forma. Os resultados indicam que em cada vértice por onde a corda passa, existe um momento de quadrupolo magnético adicional, de forma que o campo criado pela corda decai muito rapidamente.

Diese Arbeit beschreibt die Suche nach relativistischen magnetischen Monopolen mit dem AMANDA Detektor. Die Methoden der Simulation und der Untergrundseparation werden erläutert. Keine Spuren mit der Signatur eines magnetischen Monopols wurden gefunden. Das sich ergebende Flusslimit von 0.61x10^-16 1/(cm^2 sr s) für Monopole, die sich nahe der Lichtgeschwindigkeit bewegen, liegt um einen Faktor 3-4 besser als die Ergebnisse vergleichbarer Untergrundexperimente und einen Faktor 16 unterhalb der Grenze, die aus der beobachteten Stabilität der galaktischen Magnetfelder liegt. / This thesis describes the search for relativistic magnetic monopoles with the AMANDA detector. The methods of their simulation and their separation from the background are given. No tracks with the signature of a magnetic monopoles are found, resulting in an upper limit on the flux of 0.61x10^-16 1/(cm^2 sr s) for monopoles with velocities close to the speed of light. This is better by a factor of 3-4 compared to results from other underground detectors and a factor of 16 below the limit derived from the observed stability of the galactic magnetic fields.