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Following an examination of the properties of the conformal group in 4-space, a review is made of the procedure by which conformally covariant massless field equations are written in manifestly covariant form. By writing the Minkowski coordinates in terms of coordinates on the null hyperquadric of a 6-dimensional flat space with two timelike directions, the action of the group is linearized and field equations are written in rotationally covariant form in 6-dimensional space. It is then shown that extending the 6-coordinates off the null surface generalizes Minkowski space to a 5-dimensional space. Such a generalization necessitates employing a method of descent to 4-dimensional space from six dimensions which differs from the usual procedure, and allows one to encompass massive field theories in the manifest formalism. It is demonstrated that these massive fields can be understood as manifestations in Minkowski space of massless fields in 5-dimsnsional space. For the case of spinors, the field equation can accomodate precisely two species of particle having two different masses. An action principle is developed in the 6-space, and a method of field quantization is devised. As examples of the method, the special cases of spin-0, spin-1/2, and spin-1 fields are examined in detail, and minimal coupling of the spinor field equation is carried out. The formalism presented in this investigation provides a means by which one can apprehend a massive compensating field within the confines of a gauge invariant theory. The interactions which are obtained in Minkowski space include not only the usual couplings with massive vector or pseudovector fields, but as well the pseudoscalar coupling occurs automatically within this gauge invariant formulation. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

Made available in DSpace on 2016-05-17T16:50:51Z (GMT). No. of bitstreams: 0 Previous issue date: 2006-09-29. Added 1 bitstream(s) on 2016-05-17T16:54:28Z : No. of bitstreams: 1 000855054.pdf: 470877 bytes, checksum: 60b3c5b992ae7d78b6dc013884d65cfa (MD5) / Nesta tese vamos estudar dois aspectos diferentes da física da constante cosmológica: a estrutura algébrica do grupo de de Sitter, e as suas implicações na dinâmica do Universo. Na primeira parte, apresentaremos uma descrição da estrutura geométrica do espaço de de Sitter, bem como uma discussão detalhada da estrutura do grupo de de Sitter. Revisaremos os limites do grupo de de Sitter obtidos por meio do processo de contração de Inönü-Wigner, e estudaremos o limite formal 'lâmbda' 'SETA' 'INFINITO'. Neste limite, obtem-se um espaço-tempo singular, maximalmente simétrico, transitivo sob transformações conformes próprias, e com propriedades termodinâmicas que se ajustam à idéia de uma condição inicial para um Universo com big-bang. Ainda neste contexto, proporemos uma relatividade restrita baseada no grupo de de Sitter. Nesta teoria, a constante cosmológica introduz uma escala de comprimento invariante: o raio de de Sitter. A introdução desta escala invariante não implica numa violação da simetria de Lorentz, mas sim numa mudança na estrutura causal do espaço-tempo, bem como nas definições de momento e energia. Na segunda parte da tese, que trata das aplicações cosmológicas, apresentaremos um modelo dinâmico para a constante cosmológica. Neste modelo, como consequência das equações de Einstein, uma variação em 'lâmbda' deve necessariamente ser compensada pela criação ou destruição de matéria, de modo que a energia total seja mantida constante. Um modelo particular para esta evolução da constante cosmológica é apresentado, o qual está baseado no principio holográfico. Veremos como o modelo pode incorporar simultaneamente a expansão acelerada do Universo, e a coincidência na ordem de grandeza das densidades de energia escura e de matéria / In this thesis we study two different aspects of the physics of the cosmological constant: the algebraic structure of the de Sitter group, and its implications in the large scale dynamics of the Universe. In the first part we present a general description of the geometrical structure of de Sitter space, and a discussion about the structure of de Sitter group. We review the contraction limits of de Sitter group, obtained by means of the Inönü-Wigner procedure, and we study in detail the formal limit 'lâmbda' 'SETA' 'INFINITO'. In this limit, one obtains a maximally-symmetric, singular spacetime, transitive under proper conformal transformations, and with thermodynamic properties that agreee with the idea of an initial condition for a big-bang Universe. In the same context, we propose a special relativity based on the de Sitter group. In this theory, the cosmological constant introduces an invariant length scale: the de Sitter radius. The introduction of this invariant scale does not imply a violation of the Lorentz symmetry, but simply a change in the causal structure of the spacetime, as well as in the basic notions of momentum and energy. In the second part of the thesis, that related with cosmological applications, a dynamic model for the cosmological constant will be presented. In this model, as a consequence of Einstein's equations, a variation in 'lâmbda' must necessarily be compensated by creation or destruction of matterenergy, in such a way that the total energy remains constant. A particular model allowing for the evolution of the cosmological constant is presented, which is based on the holographic principle. We will show how this model can accommodate simultaneously the accelerated expansion of the Universe and the coincidence in the magnitude of matter and dark energy densities

Orientador: José Geraldo Pereira / Banca: Saulo Carneiro de Souza Silva / Banca: Mario Novello / Banca: Ruben Aldrovandi / Banca: Luis Raul Weber Abramo / Resumo: Nesta tese vamos estudar dois aspectos diferentes da física da constante cosmológica: a estrutura algébrica do grupo de de Sitter, e as suas implicações na dinâmica do Universo. Na primeira parte, apresentaremos uma descrição da estrutura geométrica do espaço de de Sitter, bem como uma discussão detalhada da estrutura do grupo de de Sitter. Revisaremos os limites do grupo de de Sitter obtidos por meio do processo de contração de Inönü-Wigner, e estudaremos o limite formal 'lâmbda' 'SETA' 'INFINITO'. Neste limite, obtem-se um espaço-tempo singular, maximalmente simétrico, transitivo sob transformações conformes próprias, e com propriedades termodinâmicas que se ajustam à idéia de uma condição inicial para um Universo com "big-bang". Ainda neste contexto, proporemos uma "relatividade restrita" baseada no grupo de de Sitter. Nesta teoria, a constante cosmológica introduz uma escala de comprimento invariante: o raio de de Sitter. A introdução desta escala invariante não implica numa violação da simetria de Lorentz, mas sim numa mudança na estrutura causal do espaço-tempo, bem como nas definições de momento e energia. Na segunda parte da tese, que trata das aplicações cosmológicas, apresentaremos um modelo dinâmico para a "constante" cosmológica. Neste modelo, como consequência das equações de Einstein, uma variação em 'lâmbda' deve necessariamente ser compensada pela criação ou destruição de matéria, de modo que a energia total seja mantida constante. Um modelo particular para esta evolução da constante cosmológica é apresentado, o qual está baseado no principio holográfico. Veremos como o modelo pode incorporar simultaneamente a expansão acelerada do Universo, e a coincidência na ordem de grandeza das densidades de energia escura e de matéria / Abstract: In this thesis we study two different aspects of the physics of the cosmological constant: the algebraic structure of the de Sitter group, and its implications in the large scale dynamics of the Universe. In the first part we present a general description of the geometrical structure of de Sitter space, and a discussion about the structure of de Sitter group. We review the contraction limits of de Sitter group, obtained by means of the Inönü-Wigner procedure, and we study in detail the formal limit 'lâmbda' 'SETA' 'INFINITO'. In this limit, one obtains a maximally-symmetric, singular spacetime, transitive under proper conformal transformations, and with thermodynamic properties that agreee with the idea of an initial condition for a "big-bang" Universe. In the same context, we propose a "special relativity" based on the de Sitter group. In this theory, the cosmological constant introduces an invariant length scale: the de Sitter radius. The introduction of this invariant scale does not imply a violation of the Lorentz symmetry, but simply a change in the causal structure of the spacetime, as well as in the basic notions of momentum and energy. In the second part of the thesis, that related with cosmological applications, a dynamic model for the cosmological "constant will be presented. In this model, as a consequence of Einstein's equations, a variation in 'lâmbda' must necessarily be compensated by creation or destruction of matterenergy, in such a way that the total energy remains constant. A particular model allowing for the evolution of the cosmological constant is presented, which is based on the holographic principle. We will show how this model can accommodate simultaneously the accelerated expansion of the Universe and the coincidence in the magnitude of matter and dark energy densities / Doutor

Let G be a complex semisimple Lie Group with parabolic subgroup P, so that G/P is a generalized flag manifold. An algebraic construction of invariant differential operators between sections of homogeneous bundles over such spaces is given and it is shown how this leads to the classification of all such operators. As an example of a process which naturally generates such operators, the algebraic Penrose transform between generalized flag manifolds is given and computed for several cases, extending standard results in Twistor Theory to higher dimensions. It is then shown how to adapt the homogeneous construction to manifolds with a certain class of tangent bundle structure, including conformal manifolds. This leads to a natural definition of invariant differential operators on such manifolds, and an algebraic method for their construction. A curved analogue of the Penrose transform is given.

Thesis (Ph.D.) in Physics--University of Maine, 2007. / Includes vita. Includes bibliographical references (leaves 109-112).

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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, 5 June 2017. / The holographic computation of extremal correlators is often frustrated by divergences. The interpretation of these divergences is incomplete. The primary goal of this study is to develop a better understanding of these divergences. Towards this end, working within the AdS/CFT correspondence we review the computation of correlators. In the field theory we review well known matrix model techniques useful to study the planar limit, as well as methods exploiting group representation theory that are useful for the computation of correlators in large N but non-planar limits. On the gravity side of the correspondence, we describe in detail the computation of two- and three point functions of a scalar field coupled to gravity on the Euclidian AdSd+1 space, three-point functions of two giant gravitons and one pointlike graviton as well as correlators of Kaluza-Klein gravitons. A key observation of this study is that extremal correlators are mapped to scattering amplitudes of particles with parallel momenta. These are naturally accompanied by involve collinear divergences. Therefore, we suggest that the divergences in the computation of extremal correlators are linked to collinear divergences. A lot more work is needed to establish this connection. / LG2017

Orientador: José Geraldo Pereira / Banc: Roldão da Rocha Junior / Banca:Marcos Vinícius Borges Teixeira Lima / Banca: Bruto Max Pimentel Escobar / Banca: Yuri N. Obukhov / Resumo: Na presença de uma constante cosmológica, interpretada como uma entidade puramente geométrica, a ausência de matéria é representada pelo espaço de de Sitter. Como consequência, a relatividade especial de Poincaré não é mais válida e deve ser substituída por uma relatividade especial baseada no grupo de de Sitter, o que produz modificações em todas as áreas da física. Nesta tese, vamos estudar os fundamentos da relatividade especial de de Sitter, bem como algumas implicações para o problema da energia escura, para a propagação de raios gama de altíssimas energias e para o espalhamento Compton. Como um subproduto desses estudos, desenvolvemos um novo método de se obter equações de campo com invariância conforme, o qual faz uso dos invariantes de Casimir do grupo de de Sitter. Usando esse novo método, fazemos um estudo crítico das equações que descrevem um campo fundamental de spin-2 / Abstract: The presence of a cosmological constant, interpreted as a purely geometric entity, absence of matter ir represented by a de Sitter spacetime. As a consequence, ordinary Poincaré specil relativity is no longer valid and must be replaced by a special relativity based on the de Sitter group, which produces concomitant changes in all areas of physics. In this thesis, we are going to explore the implications for the dark energy problem, for the propagation of ultra high-energy gamma rays, and for the Compton scattering formula. As a byoproduct of these studies, we developed a new method for obtaining conformal invariant fiels equations, which makes use of the Casimir operators of the de Sitter group. Using this new method, we make a critical review of the fiels equations describing a fundamental spin-2 field / Doutor

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