Among a number of fundamental issues, the origin of inertial mass remains one of the major open problems in particle physics. Furthermore, topological effects related to non perturbative field configurations are poorly understood in those gauge theories of direct relevance to our physical universe. Motivated by such issues, this Thesis provides a deeper understanding for the appearance of topological effects in abelian gauge field theories, also in relation to the existence of a mass gap for the gauge interactions. These effects are not accounted for when proceeding through gauge fixings as is customary in the literature. The original Topological-Physical factorisation put forth in this work enables to properly identify in topologically massive gauge theories (TMGT) a topological sector which appears under formal limits within the Lagrangian formulation. Our factorisation then allows for a straightforward quantisation of TMGT, accounting for all the topological features inherent to such dynamics. Moreover dual actions are constructed while preserving the gauge symmetry also in the presence of dielectric couplings. All the celebrated mass generation mechanisms preserving the gauge symmetry are then recovered but now find their rightful place through a network of dualities, modulo the presence of topological terms generating topological effects. In particular a dual formulation of the famous Nielsen-Olesen vortices is constructed from TMGT. Within a novel physically equivalent picture, these topological defects are interpreted as dielectric monopoles.

In this work we will try to quantize midisuperspace model of spherically sym- metric spacetime with massless scalar field. On this type of spacetimes we apply Dirac method of canonical quantization, leading to Wheeler-DeWitt equations. We will attempt to solve those equation generally for aforementioned type of spa- cetimes. Our initial midisuperspace model is Roberts dynamical spacetime. As we will see later, Roberts metric behaves badly in the asymptotic region. Due to this problematic behaviour of Roberts spacetime at the boundary, we will choose to quantize its static version, the special Janis-Newman-Winicour spacetime. This midisuperspace model is static, asymptotically flat spacetime with scalar field and it contains a naked time-like singularity. For special Janis-Newman-Winicour spacetime we will then solve Wheeler-DeWitt equations.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-04-26T17:48:21Z No. of bitstreams: 1 brunoferreirarizzuti.pdf: 507162 bytes, checksum: 6ccfc7f9025a41c3c8bc647f63d413ea (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-05-13T12:04:02Z (GMT) No. of bitstreams: 1 brunoferreirarizzuti.pdf: 507162 bytes, checksum: 6ccfc7f9025a41c3c8bc647f63d413ea (MD5) / Made available in DSpace on 2017-05-13T12:04:02Z (GMT). No. of bitstreams: 1 brunoferreirarizzuti.pdf: 507162 bytes, checksum: 6ccfc7f9025a41c3c8bc647f63d413ea (MD5) Previous issue date: 2012-02-29 / Passados mais de 60 anos da sua formulação inicial, o método de Dirac-Bergmann para hamiltonização de sistemas lagrangianos singulares continua sendo uma ferramenta poderosa para análise e investigação de modelos atuais de física teórica. Como motivação, apresentaremos vários exemplos onde o método é utilizado e o descreveremos em detalhes em uma sequência de passos. O objetivo central deste trabalho será então apresentar uma série de aplicações distintas do método de Dirac, incluindo a busca de simetrias locais para teorias singulares, a construção da proposta de relatividade especial dupla de Magueijo-Smolin, a formulação da mecânica clássica com invariância de reparametrizações e sua quantização e por fim, discutiremos um modelo semiclássico mecânico que, quando quantizado, reproduz a equação de Dirac. / After more than 60 years of its initial development, the Dirac-Bergmann method for hamiltonization of constrained systems is still a powerful tool for analysis and investigation of modern theoretical models. As a motivation, we shall present several models where the method is applied, then we will describe it in details, with a sequence of steps. The main objective of this work is to provide distinct applications of the Dirac method, including the search for local symmetries of singular theories, the construction of the Magueijo-Smolin doubly special relativity proposal, the formulation of classical mechanics with reparametrization invariance and its quantization and finally, we discuss a semiclassical mechanical model that produces the Dirac equation through quantization.

Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-10-10T14:48:12Z No. of bitstreams: 1 guilhermeenriquealemanlopez.pdf: 6728480 bytes, checksum: d96cb4f60e6df31a85d6b383dec056f1 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-10-16T13:35:18Z (GMT) No. of bitstreams: 1 guilhermeenriquealemanlopez.pdf: 6728480 bytes, checksum: d96cb4f60e6df31a85d6b383dec056f1 (MD5) / Made available in DSpace on 2018-10-16T13:35:18Z (GMT). No. of bitstreams: 1 guilhermeenriquealemanlopez.pdf: 6728480 bytes, checksum: d96cb4f60e6df31a85d6b383dec056f1 (MD5) Previous issue date: 2018-08-24 / O objetivo deste trabalho é o estudo de procedimento de quantização canônica de uma partícula em um espaço curvo e sobre uma superfície de espaço Euclidiano. Estudaremos quantização canônica em coordenadas curvilineares, e em seguida vamos adaptar no caso de espaço curvo. Fizemos comparação crítica deste formalismo com três procedimentos principais apresentados na literatura desta área. / The aim of this work is to study the canonical quantization procedure of a particle in a Riemann space, as well as on a surface embedded in Euclidean space. To this aim, we rewrite quantum mechanics of a particle in Euclidean space in curvilinear coordinates. This allows us to formulate certain quantization procedure in a Riemann space. The resulting picture is compared with three quantization proposals known in the literature.

Over a century since its inception, general relativity continues to lie at the heart of some of the most researched topics in theoretical physics. It seems likely that the coveted solutions to problems like quantum gravity are to be found in an extension of general relativity, one which may only be visible in an alternate formulation of the theory.  In this thesis we consider the possibility of casting general relativity in the form of an initial value problem where spacetime is seen as the evolution of space. This evolution is shown to be constrained and of Hamiltonian type.  Not all spacetimes are physically acceptable. To be compatible with particle physics, one would like spacetime to accommodate fermions. Here we can take comfort in Geroch’s theorem, which implies that any spacetime that admits a Hamiltonian formulation automatically supports the existence of fermions. We review the elements that go into the proof of this theorem. / Allmän relativitetsteori har i över hundra år legat i teoretiska fysikens framkant. Det är möjligt att lösningarna på öppna problem som kvantiseringen av gravitation går att finna i en utvidgning av allmän relativitetsteori – och kanske uppenbarar sig denna utvidgning bara ur en alternativ formulering av teorin. I den här uppsatsen formuleras allmän relativitetsteori och dess Einsteinekvationer som ett begynnelsevärdesproblem, genom vilket rumtiden kan betraktas som rummets historia. Vi visar att rummets rörelseekvationer är Hamiltons ekvationer med tvångsvillkor.  Enligt partikelfysiken bör fermioner kunna finnas till i rumtiden. Härom kan vi åberopa Gerochs sats, enligt vilken rumtider som har en Hamiltonsk formulering också medger fermioner. Vi redogör för huvuddragen i beviset av Gerochs sats.