Submitted by Rosivalda Pereira (mrs.pereira@ufma.br) on 2017-06-07T18:34:00Z No. of bitstreams: 1 FredericoSantos.pdf: 963672 bytes, checksum: 82f7ae1b28b9c136b94c6c04439b8c32 (MD5) / Made available in DSpace on 2017-06-07T18:34:00Z (GMT). No. of bitstreams: 1 FredericoSantos.pdf: 963672 bytes, checksum: 82f7ae1b28b9c136b94c6c04439b8c32 (MD5) Previous issue date: 2010-12-15 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Fundação de Amparo à Pesquisa e ao Desenvolvimento Científico e Tecnológico do Maranhão (FAPEMA) / The standard model extension is a theoretical framework which includes the possibility of Lorentz symmetry violation in the Standard Model of elementary interactions. In electrodynamics, this possibility is represented by the term, Kμν∝βFμνF∝β , that violates Lorentz symmetry without jeopardizing CPT symmetry, and the term ε∝μβνV∝Aμ∂βAν, which violates Lorentz and CPT symmetries. These additional terms are inserted in the Maxwell Lagrangena and alter the field equations, as well. In this work we study the influence of Lorentz violation in the photonic sector on fermion scattering processes, regarding individually the CPT-odd and CPT-even coefficients. At first, we present a review through some topics of great interest, as the Dirac equation, Dirac propagator, scattering matrix, Feynman rules, Casimir trick, and the evaluation of the differential cross sections. Next, we implemented the developed techniques to carry out the corrections (to the cross sections) induced by the Lorentz-violating terms. Our results reveal as each Lorentz-violating component changes the cross section. In the CPT-even case, we observed that the contribution of the term tr to the process e− + μ− → e− + μ− is of difficult detection once it can be disguised between the radioactive corrections. The contributions coming from the vector i imply an angular dependence in the differential cross section of the process e− + μ− → e− + μ−, and do not contribute for the process e− + e+ → μ− + μ+. The CPT-even coefficients, (Ke−)ij , lead to significant contributions in both cases. We highlight its influence in the pair electron-positron annihilation process, where they act as the only components that imply sensitive contributions. The contribution stemming from the CPT-odd sector, represented by the Carroll-Field-Jackiw term, is of less relevance, since the contribute are second order ones. Although we have initially developed a perturbative procedure for evaluating the cross section correction, it was also possible to evaluate the exact propagators of the CPT-odd and CPT-even sectors in a tensor closed form. Such tensor expressions may be used to rederive the cross section corrections. / O Modelo Padrão Estendido (MPE)é um arcabouço teórico que considera a possibilidade de violação de simetria de Lorentz no Modelo Padrão das interações elementares. Na eletrodinâmica, esta possibilidade é representada pelo termo Kμν∝βFμνF∝β , que viola a simetria de Lorentz sem violar a simetria CPT, e o termo ε∝μβνV∝Aμ∂βAν, que viola a simetria de Lorentz, juntamente com a simetria CPT. Estes termos extras são incluídos na lagrangena de Maxwell e, consequentemente, também alteram a equação de movimento dos campos. Neste trabalho consideramos a influência da violação de Lorentz no setor fotônico em processos de espalhamento de férmions, e− + μ− ! e− + μ− e e− + e+ ! μ− + μ+, considerando individualmente o setor CPT-ímpar e CPT-par em suas componentes não-birrefringentes. No primeiro momento, apresentamos uma revisão de tópicos de interesse, passando pela equação de Dirac, propagador de Dirac, matriz de espalhamento, regras de Feynman, truque de Casimir, finalizando com o cálculo das seções de choque diferenciais para processos elementares. Em seguida, implementamos as técnicas desenvolvidas para calcular o incremento à seção de choque, oriundo da violação de simetria de Lorentz no setor fotônico. Em nossos resultados, obtivemos como cada componente de violação de Lorentz altera a seção de choque. No caso CPT-par, observamos que a contribuição do termo Kir ao processo e− + e+ → μ− + μ+ é de difícil verificação, pois se confunde com as contribuições radioativas. Já as contribuições advindas do vetor Ki, inserem uma dependência angular na seção de choque diferencial do processo e− + μ− → e− + μ−, mas não contribui no processo e− + e+ → μ− + μ+. Os coeficientes paridade-par, (Ke−)ij , implicam em contribuições relevantes em ambos os processos, e destacamos sua influência no processo de aniquilação elétron-pósitron, onde atuam como únicas componentes que contribuem de forma notável. A contribuição do setor CPT-ímpar (termo de Carroll-Field-Jackiw) é comparativamente de menor relevância, já que as contribuições à seção de choque aparecem apenas em segunda ordem. Embora tenhamos inicialmente desenvolvido um procedimento perturbativo para calcular as contribuições dos parâmetros de quebra de Lorentz à seção de choque, também foi possível obter os propagadores de Feynman exatos tanto para o setor CPT-ímpar quanto para o setor CPT-par. Tais expressões podem ser usadas para recalcular as seções de choque.

Second-order phase transitions involve critical fluctuations just below and above the transition temperature. Macroscopically, they manifest in the power-law behaviour of many physical properties such as the susceptibility and the specific heat. The power-laws are predicted to be universal, i.e. the same exponents are expected for a certain class of transitions irrespective of the microscopic details of the system. The underlying commonality of such transitions is the divergence of the correlation length ξ and the correlation time ξ_τ of the critical fluctuations at the transition temperature. Both ξ and ξ_τ can be directly observed by neutron scattering experiments, making them an ideal tool for the study of critical phenomena. At classical phase transitions, the critical fluctuations will be thermal in nature. However, if a second-order transition occurs at T = 0, thermal fluctuations are frozen, and the transition is driven by quantum fluctuations instead. This is called a quantum critical point. The quantum nature of the fluctuations influences observable properties, also at finite temperatures, and causes unusual behaviour in the vicinity of the quantum critical point or the existence of exotic phases, e.g. unconventional superconductivity. Heavy-fermion compounds are a class of materials that is well suited for the study of quantum criticality. They frequently show second-order transitions into a magnetically ordered state at very low temperatures, which can easily be tuned to T = 0 by the application of pressure, magnetic fields or element substitution. In this thesis, fluctuations near a quantum critical point are investigated for three heavy-fermion systems. CeCu2Si2 shows unconventional superconductivity close to an antiferromagnetic quantum critical point. Results from single-crystal neutron spectroscopy and thermodynamic measurements are discussed and some details are also given about the synthesis of large single crystals. The focus of the study is the comparison of the inelastic response of magnetic and superconducting samples, which are found to be very similar for ΔE > 0.2 meV. CePdAl has an antiferromagnetic state with partial magnetic frustration. The ordering temperature can be suppressed by Ni substitution towards a quantum critical point. Single-crystal neutron diffraction experiments of three members of the substitution series were analysed. They revealed several unusual effects of the frustrated state in the pure sample, and show that magnetic order and frustration persist in the substituted samples. YbNi4P2 is a rare example of a compound with ferromagnetic quantum criticality, which has only been studied in the last few years. The aim of the powder neutron spectroscopy experiments presented here was to obtain an overview of the relevant energy scales, i.e. the crystal electric field, local magnetic fluctuations and ferromagnetic fluctuations. Simulations using the program McPhase were performed for a thorough understanding of the crystal electric field.