BDTD - Biblioteca Digital de Teses e Dissertações
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Doctoral Thesis Vínculos de eletrodinâmicas não lineares(2018-12-14) Akmansoy, Pierre Niau; Medeiros, Leo Gouvea; ; ; Queiroz, Farinaldo da Silva; ; Viti, Jacopo; ; Escobar, Bruto Max Pimentel; ; Bufalo, Rodrigo Santos;Nonlinear electrodynamics (NLED) are a generalization of Maxwell’s electrodynamics that arises and is used in several fields such as: gravitation, classical consequences of the quantum vacuum, low energy limits of string theories etc. Because of this, it is an important task to evaluate the empirical validity of these theories by comparing their predictions with the corresponding experimental measurements. In this thesis, the ionization energy of the hydrogen atom and the photon-photon scattering cross section recently observed by the ATLAS Collaboration with ultraperipheral collisions of lead ions are used. The way in which Born-Infeld-like theories, a class of NLED, modify the Coulomb potential produced by the hydrogen atom’s nucleus is calculated. Then, using the perturbation theory, the first order correction of the ground state energy is derived. It is remarkable that, although this class of NLED behaves identically in the low energy limit, each theory produces a slightly different correction. This is due to the framework of perturbation theory which forces the use of the complete Lagrangian. Comparison with the measurement of the ionization energy constrains the parameter b, which characterizes this class of theories, to be b & 1021V m−1 . The direct interaction between photons is one of the most striking features of NLED. Therefore, the cross section for γγ → γγ scattering acquires a contribution due to nonlinear corrections to Maxwell’s Lagrangian besides the Standard Model ones. In the equivalent photon approximation, the complete scattering cross section for Pb Pb → Pb Pb + γγ in ultraperipheral collisions is derived through the convolution of the subprocess cross section γγ → γγ with the photon fluxes produced by the ions. Comparison of the complete cross section with the experimental measurement obtained by the ATLAS Collaboration yields the most precise constrain for the nonlinear parameters α ∼ β . 2 × 10−10GeV−4 ≈ 10−47m3 J −1.Master Thesis Termodinâmica de um gás de fótons no contexto de eletrodinâmicas não-lineares(Universidade Federal do Rio Grande do Norte, 2014-03-31) Akmansoy, Pierre Niau; Medeiros, Léo Gouvêa; ; http://lattes.cnpq.br/2797502202617114; ; http://lattes.cnpq.br/5497346855973593; Silva Júnior, Raimundo; ; http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4790590E2; Cuzinatto, Rodrigo Rocha; ; http://lattes.cnpq.br/8073303573679522The objective of this dissertation is the development of a general formalism to analyze the thermodynamical properties of a photon gas under the context of nonlinear electrodynamics (NLED). To this end it is obtained, through the systematic analysis of Maxwell s electromagnetism (EM) properties, the general dependence of the Lagrangian that describes this kind of theories. From this Lagrangian and in the background of classical field theory, we derive the general dispersion relation that photons must obey in terms of a background field and the NLED properties. It is important to note that, in order to achieve this result, an aproximation has been made in order to allow the separation of the total electromagnetic field into a strong background electromagnetic field and a perturbation. Once the dispersion relation is in hand, the usual Bose-Einstein statistical procedure is followed through which the thermodynamical properties, energy density and pressure relations are obtained. An important result of this work is the fact that equation of state remains identical to the one obtained under EM. Then, two examples are made where the thermodynamic properties are explicitly derived in the context of two NLED, Born-Infelds and a quadratic approximation. The choice of the first one is due to the vast appearance in literature and, the second one, because it is a first order approximation of a large class of NLED. Ultimately, both are chosen because of their simplicity. Finally, the results are compared to EM and interpreted, suggesting possible tests to verify the internal consistency of NLED and motivating further developement into the formalism s quantum case