https://repositorio.ufpb.br/jspui/handle/tede/5435 PPGF 2026-08-03T13:46:06Z https://repositorio.ufpb.br/jspui/handle/123456789/38517 Título: Potencial efetivo nas teorias tipo Hořava–Lifshitz Autor(es): Lima, André Manzoni de Orientador: Petrov, Albert Abstract: In the beggining of the 20th century, Quantum Mechanics and Special Relativity changed radically the basic notions of physics. From the merging of the two theories Quantum Field Theory was born, the basis of the Standard Model of Elementary Particles, which describes three of the four fundamental interactions (electromagnetic and the strong and weak forces). The gravitational interaction is described in a very different setting, namelly the classical General Theory of Relativity, whose formulation is quite distinct from the one used for the other interactions. Initial efforts to place the four interactions into the same conceptual framework were unsuccessful. The reason behind it is that, if treated as a quantum field theory, gravity yields divergent results. Several theories were presented as candidates to put gravity at the same footing as other interactions. One of these theories, proposed by Petr Horava in 2009, consists in enhancing the divergence properties of quantum gravity through the introduction of an anisotropic space-time. As Horava’s proposal changes the notions of space and time essentially, one may ask questions about how the usual quantum field theory models behave under such changes. In this thesis we study two quantum field theory models within the context of Horava-like space-time anisotropy. We calculate the effective potential at one loop order for the scalar QED using two methods. The first, Dirac’s method for constrained systems, does not reffer to any type of gauge choice. In the second method we studied the model with a particular choice of gauge fixing, which led to the appearance of Faddeev-Popov ghosts. We have also studied the Gross-Neveu model, for which we calculated the gap equation, showing the dynamical parity breaking and mass generation under specific circumstances. We calculated the gap equation in the finite temperature case, having found the critical temperature for which the parity breaking occurs. We have also analized the renormalization properties of the theory in the 1=N expasion. Finally, we checked for the possibility of generating the Chern-Simons term for this Gross- Neveu model. Editor: Universidade Federal da Paraíba Tipo: Tese 2018-02-27T00:00:00Z https://repositorio.ufpb.br/jspui/handle/123456789/38432 Título: HIgh-energy astroparticle physics as a window into quantum gravity Autor(es): Morais, Pedro Henrique Orientador: Bezerra, Valdir Barbosa Abstract: The search for quantum gravity signatures in astrophysical observations is one of the central challenges of modern physics. In this thesis, we investigate the phenomenological consequences of scenarios that violate or deform Lorentz symmetries, focusing on extremely high-energy particles produced by cosmic rays and extragalactic sources. We employ a kinematical framework based on Finsler geometry, which enables the description of modified dispersion relations and momentum conservation laws compatible with κ-Poincaré–type symmetries. This approach leads to deformed Lorentz transformations containing terms that are amplified by the particle’s energy, opening the possibility of enhancing Planck-scale effects. The thesis emphasizes two main directions. The first concerns modifications to the lifetimes of relativistic particles, such as muons and pions. Along this line, we show that time dilation receives specific corrections in deformed relativity scenarios, making particle lifetimes a promising observable for experimental tests, whether in muon beam experiments or atmospheric showers. The second direction examines the kinematics of two-body decays, especially π →μ +ν, considering different momentum composition laws compatible with Deformed Special Relativity (DSR). Although the corrections are small, they can affect the relative production of muons and neutrinos in showers initiated by ultra-high-energy cosmic rays, contributing to the ongoing discussion of the muon puzzle. We also investigate the extragalactic and atmospheric propagation of ultra-high-energy photons, whose behavior is sensitive to alterations in the dispersion relation. In Lorentz Invariance Violation (LIV)/DSR scenarios, processes such as pair production may have their thresholds shifted, modifying the transparency horizon of the Universe and potentially altering the development of gamma-ray induced atmospheric showers. The results indicate that extremely high-energy astrophysical messengers—atmospheric muons, neutrinos, and ultra-high-energy photons—provide a privileged laboratory for probing quantum spacetime effects. Thus, this thesis establishes a coherent phenomenological framework linking models of modified relativity with observations in particle astrophysics, highlighting realistic observational avenues for testing quantum gravity hypotheses. Editor: Universidade Federal da Paraíba Tipo: Tese 2026-02-27T00:00:00Z https://repositorio.ufpb.br/jspui/handle/123456789/38357 Título: Quantum dynamics beyond lorentz invariance Autor(es): Silva, Gislaine Varão da Orientador: Bezerra, Valdir Barbosa Abstract: Many approaches to quantum gravity predict the existence of a minimal length associated with the Planck scale, leading to modifications in the relations between energy, momentum, and position, which may in turn affect Lorentz symmetry. In this thesis, we investigate these effects in both systematic and stochastic scenarios, with particular emphasis on their low-energy manifestations. In the first part, we analyze systematic effects derived from modified dispersion relations (MDRs) motivated by quantum gravity. We show that the nonrelativistic limit of general MDRs leads to a deformed nonrelativistic Schrödinger equation containing fractional and nonlocal terms in the Hamiltonian. These terms modify quantum kinematics and allow the establishment of experimental bounds on MDR parameters using low-energy systems. We further demonstrate that certain MDRs with fractional powers give rise to a dynamics described by fractional quantum mechanics at low energies, associated with an effectively fractal geometry in the infrared. We also study stochastic effects associated with Planck-scale fluctuations in MDRs, modeling a stochastic violation of Lorentz symmetry. Performing the stochastic average leads to a Lindblad equation that describes a mechanism of gravitational decoherence in the nonrelativistic regime. We apply this formalism to gravitational Schrödinger cat states (gravcats), revealing the competition between gravitationally induced entanglement and decoherence driven by Planckian fluctuations, and allowing us to estimate the scales at which such effects become relevant. In the second part, we analyze an additional scenario based on noncommutative spacetimes, showing that the deformation of the energy composition rule characteristic of the κ-Minkowski spacetime induces quantum correlations between two systems, even in the nonrelativistic limit. These results demonstrate that low-energy quantum systems provide a novel avenue to test Lorentz symmetry, either through systematic deformations or stochastic violations. The infrared regime has the potential to amplify Planck-suppressed corrections, thereby providing new opportunities to test effective quantum gravity models in tabletop experiments. Editor: Universidade Federal da Paraíba Tipo: Tese 2026-02-23T00:00:00Z https://repositorio.ufpb.br/jspui/handle/123456789/37676 Título: Influência conjunta da polarização e da coerência da luz no experimento da dupla fenda sob uma perspectiva quântica Autor(es): Barbosa, Natália Érika Laurentino Orientador: Bernardo, Bertúlio de Lima Abstract: In this research, we studied the wave-particle duality through quantifiers of visibility and distuinguishability by the complementary principle. We used the unified density matrix formalism of coherence and polarization as the basis for this study. If we have information on the path, the interference pattern is destroyed and the photon behaves like a particle, on the other hand, a maximum contrast pattern is verified when there is no information on the path taken, a wave-like behavior. To witness the wave-particle duality using the visibility V and distinguishability D quantifiers derived in the research, we present several physical examples and show that it is possible to verify the behavior of photons, quantified through the principle of complementarity by means of the inequality D2 + V 2 ≤ 1. Editor: Universidade Federal da Paraíba Tipo: Dissertação 2020-07-29T00:00:00Z