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Teoria de Dirac modificada no Modelo Padrão Estendido não-mínimo. / Dirac theory modified in Standard Model Non-minimal extended.REIS, João Alfíeres Andrade de Simões dos 22 February 2017 (has links)
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Previous issue date: 2017-02-22 / CAPES. / For the recent years, there has been a growing interest in Lorentz-violating theories.
Studies have been carried out addressing the inclusion of Lorentz-violating
terms into the Standard Model (SM). This has led to the development of the Standard
Model Extension (SME), which is a framework containing modifications that
are power-counting renormalizable and consistent with the gauge structure of the
SM. More recently, a nonminimal version of the SME was developed for the photon,
neutrino, and fermion sector additionally including higher-derivative terms. One
of the new properties of this nonminimal version is the lost of renormalizability.
In this work, we study the main aspects of a modified Dirac theory in the nonminimal
Standard-Model Extension. We focus on two types of operators namely,
pseudovector and two-tensor operators. These two operators display an unusual
property; they break the degeneracy of spin. This new property becomes manifest
in providing two di erent dispersion relations, one for each spin projection. To
solve the Dirac equation modified by those operators, we introduce a new method
that was suggested by Kostelecký and Mewes in a recent research paper. This
method allows to block-diagonalizing the modified Dirac equation and, thus, permits
us to obtain the spinors. The objectives of the current work are as follows.
First, we will review the main concepts for understanding the SME. Second, we
will introduce how to extend the minimal fermion sector to the nonminimal one.
Third, we will describe the method that block-diagonalizes the modified Dirac
equation and we will compute the field equations. And,finally, we will get the
exact dispersion relations and the spinor solutions for operators of arbitrary mass
dimension. / Nos últimos anos, houve um aumento significativo no interesse em teorias que
violam a simetria de Lorentz. Estudos têm sido realizados na tentativa de incluir
termos que violam a simetria de Lorentz no Modelo Padrão (MP). Esta tentativa
culminou no surgimento do chamado Modelo Padrão Estendido (MPE). Este modelo
contempla todas as possíveis modificações que são consistentes com as propriedades
já bem estabelecidas, tais como renormalizabilidade e a estrutura de gauge
do MP. Mais recentemente, uma versão não-mínima do MPE foi desenvolvida
para os setores dos fótons, neutrinos e para os férmions. Esta versão não-mínima
caracteriza-se pela presença de altas derivadas. Uma das novas propriedades nesta
versão não-mínima é a perda da renormalizabilidade.
Neste trabalho, estudamos os principais aspectos da teoria de Dirac modi cada
no MPE não-mínimo. Nós nos concentramos em dois tipos de operadores a saber,
operadores pseudovetoriais e tensoriais. Estes dois operadores exibem uma propriedade
incomum, eles quebram a degenerescência de spin. Esta nova propriedade
manifesta-se, por exemplo, na presença de duas relações de dispersão diferentes,
uma para cada projeção do spin. Para resolver a equação de Dirac modi cada por
esses operadores, introduzimos um novo método que foi sugerido por Kostelecký e
Mewes em um trabalho recente. Este método permite bloco-diagonalizar a equação
de Dirac modi cada e, assim, nos fornece uma nova maneira de obter os espinores.
Os objetivos do presente trabalho são os seguintes. Primeiro, iremos rever alguns
conceitos essenciais para o entendimento do MPE. Segundo, apresentaremos a extens
ão do setor fermiônico mínimo para o não-mínimo. Terceiro, descreveremos
o método que bloco-diagonaliza a equação de Dirac modi cada e calcularemos as
equações de campo. Por fim, calcularemos as relações de dispersão exatas e as
soluções espinoriais para cada configuração não-mínima dos operadores citados.
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Propriétés spectrales de l'opérateur de Dirac avec un champ magnétique intenseSourisse, Arnaud 30 June 2006 (has links) (PDF)
On étudie l'opérateur de Dirac bidimensionnel avec un champ magnétique tendant vers l'infini en l'infini. Le spectre d'un tel opérateur est uniquement composé de valeurs propres et en particulier le spectre essentiel est réduit à un point. Pour un champ magnétique à croissance polynomiale, on donne l'équivalent des valeurs propres à l'infini.<br />Quand on perturbe cet opérateur par un potentiel électrique tendant vers zéro à l'infini avec une décroissance polynomiale, exponentielle ou à support compact, des valeurs propres sont créées près du point du spectre essentiel. On étudie le comportement asymptotique du spectre discret de l'opérateur perturbé près de ce point.<br />Pour l'opérateur de Dirac tridimensionnel avec un champ magnétique constant, on définit les résonances à l'aide de la méthode de dilatation analytique. Grâce à la méthode de Grushin, on étudie les résonances près des niveaux de Landau-Dirac à l'aide d'un hamiltonien effectif.
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Riemannian Geometry of Quantum Groups and Finite Groups withShahn Majid, Andreas.Cap@esi.ac.at 21 June 2000 (has links)
No description available.
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L2 Index Theory and D-Particle Binding in Type I' String TheoryMcCarthy, Janice Marie January 2009 (has links)
<p>In this work, we apply $L^2$-index theory to compute the index of a non-Fredholm elliptic operator. The operator arises in Type I' string theory, and the index is found to be non-zero, thus implying existence of bound states.</p> / Dissertation
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Rigidité des hypersurfaces en géométrie riemannienne et spinorielle aspect extrinsèque et intrinsèque /Roth, Julien Hijazi, Oussama. Grosjean, Jean-François. January 2006 (has links) (PDF)
Thèse doctorat : Mathématiques : Nancy 1 : 2006. / Titre provenant de l'écran-titre.
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Local elliptic boundary value problems for the dirac operatorScholl, Matthew Gregory 28 August 2008 (has links)
Not available / text
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Nonlinear spinor fields : toward a field theory of the electronMathieu, Pierre. January 1983 (has links)
Nonlinear Dirac equations exhibiting soliton phenomena are studied. Conditions are derived for the existence of solitons and an analysis of their stability is presented. New results are obtained for models previously considered in the literature. A particular model is studied for which all stationary states are localized in a finite domain and have positive energy but indefinite charge. The electromagnetic field is introduced by minimal coupling and it is shown that the discrete nature of the electric charge, and of the angular momentum, follow from a many-body stability principle. This principle also implies the de Broglie frequency relation, and furnishes an expression for the fine structure constant. The resulting charged soliton is tentatively identified with the electron.
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Dirac generalized function : an alternative to the change of variable techniqueLopa, Samia H. January 2000 (has links)
Finding the distribution of a statistic is always an important problem that we face in statistical inference. Methods that are usually used for solving this problem are change of variable technique, distribution function technique and moment generating function technique. Among these methods change of variable technique is the most commonly used one. This method is simple when the statistic is a one-to-one transformation of the sample observations and if it is many-to-one, then one needs to compute the jacobian for each partition of the range for which the transformation is one-to-one. In addition, if we want to find the distribution of a statistic involving n random variables using the change of variable technique, we have to define (n-1) auxiliary variables. Unless these (n-1) auxiliary variables are carefully chosen, calculation of jacobian as well as finding the range of integration to obtain the marginal distribution of the statistic of interest become complicated. [See [3]]Au, Chi and Tam, Judy [1] proposed an alternative method of finding the distribution of a statistic by using Dirac generalized function. In this study we considera number of problems involving different probability distributions that are not quiet easy to solve by change of variable technique. We will illustrate the method by solving problems which include finding the distributions of sums, products, differences and ratios of random variables. The main purpose of the thesis is to show that using Dirac generalized function one can solve these problems with more ease. This alternative approach would be more suitable for students with limited mathematical background. / Department of Mathematical Sciences
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Modelle relativistischer und nicht-relativistischer Coulomb-SystemeHuber, Matthias January 2008 (has links)
Zugl.: München, Univ., Diss., 2008
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Parameteruntersuchungen an Dirac-ModellenThumstädter, Torsten. January 2003 (has links) (PDF)
Mannheim, Univ., Diss., 2003.
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