On open access repositories Creative Commons Attribution License CC-BY 4.0 Published source must be acknowledged Publisher's version/PDF may be used / 京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第19498号 / 理博第4158号 / 新制||理||1597(附属図書館) / 32534 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 國友 浩, 教授 田中 貴浩, 教授 杉本 茂樹 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

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A research project submitted to the Faculty of Science, University of the Witwatersrand, in fulfillment for the degree of Master of Science in Physics. May 25, 2017. / This project addresses the study of the memory effect. We review the effect in electromagnetism, which is an abelian gauge theory. We prove that we can shift the phase factor by performing a gauge transformation. The gauge group is U(1). We extend the study to the nonabelian gauge theory by computing the memory in SU(2) which vanishes up to the first order Taylor expansion. Keywords: Memory Effect, Aharonov-Bohm effect, Nonabelian Gauge Theory, Supersymmetry / GR2018

Calculamos as funções de Green térmicas de um e dois grávitons em um \"loop\" no \"gauge\" temporal. Para tratar os polos extras que surgem neste \"gauge\" utilizamos uma técnica livre de ambiguidades no formalismo de tempo imaginário. Foram calculadas, para temperaturas altas comparadas com o momento externo e menores que a escala de Plank, as contribuições dominantes T4 e sub-dominantes T2 e log(T) para a auto-energia do gráviton. Mostramos que as contribuições dos polos extras não modificam o comportamento das contribuições dominantes e sub-dominantes em altas temperaturas. Verificamos que os termos dominantes T4 não dependem do parâmetro de \"gauge\". Verificamos também que as identidades de \' t Hooft são satisfeitas pelos termos T2 e mostramos que o termos log(T) tem a mesma estrutura que o resíduo do polo ultravioleta da auto-energia a temperatura zero. Calculamos as relações de dispersão no plasma de grávitons até a ordem GT2 e discutimos a dependência de \"gauge\" induzida pelos termos T 2 da auto-energia. Calculamos também a função de um gráviton em dois \"loops\" em duas classes distintas de \"gauge\". / We have computed the thermal one-graviton function and the self-energy in oneloop using a temporal gauge. In order to deal with the extra poles which are present in the temporal gauge, we employ an ambiguity-free technique in the imaginary-time formalismo We obtain, for temperatures T high compared with the externaI momentum and well below the Plank scale, the leading T4 as well as the sub-Ieading T2 and log(T) contributions to the graviton self-energy. We show that the extra pole contributions do not change the behaviour of the leading and sub-Ieading contributions from hard thermal loop region. We verify that the leading contributions are gauge independent. We also verify the t Hooft identities for the sub-Ieading T 2 terms and show that the logarithmic part has the same structure as the residue of ultraviolet pole of zero temperature graviton self-energy. We compute the dispersion relations up to GT2 order and we discuss the gauge dependence induced by sub-Ieading contributions T 2. We also compute the thermal one-graviton Green\'s function in the two-Ioop approximation for two distinct gauge classes.

Calculamos as funções de Green térmicas de um e dois grávitons em um \"loop\" no \"gauge\" temporal. Para tratar os polos extras que surgem neste \"gauge\" utilizamos uma técnica livre de ambiguidades no formalismo de tempo imaginário. Foram calculadas, para temperaturas altas comparadas com o momento externo e menores que a escala de Plank, as contribuições dominantes T4 e sub-dominantes T2 e log(T) para a auto-energia do gráviton. Mostramos que as contribuições dos polos extras não modificam o comportamento das contribuições dominantes e sub-dominantes em altas temperaturas. Verificamos que os termos dominantes T4 não dependem do parâmetro de \"gauge\". Verificamos também que as identidades de \' t Hooft são satisfeitas pelos termos T2 e mostramos que o termos log(T) tem a mesma estrutura que o resíduo do polo ultravioleta da auto-energia a temperatura zero. Calculamos as relações de dispersão no plasma de grávitons até a ordem GT2 e discutimos a dependência de \"gauge\" induzida pelos termos T 2 da auto-energia. Calculamos também a função de um gráviton em dois \"loops\" em duas classes distintas de \"gauge\". / We have computed the thermal one-graviton function and the self-energy in oneloop using a temporal gauge. In order to deal with the extra poles which are present in the temporal gauge, we employ an ambiguity-free technique in the imaginary-time formalismo We obtain, for temperatures T high compared with the externaI momentum and well below the Plank scale, the leading T4 as well as the sub-Ieading T2 and log(T) contributions to the graviton self-energy. We show that the extra pole contributions do not change the behaviour of the leading and sub-Ieading contributions from hard thermal loop region. We verify that the leading contributions are gauge independent. We also verify the t Hooft identities for the sub-Ieading T 2 terms and show that the logarithmic part has the same structure as the residue of ultraviolet pole of zero temperature graviton self-energy. We compute the dispersion relations up to GT2 order and we discuss the gauge dependence induced by sub-Ieading contributions T 2. We also compute the thermal one-graviton Green\'s function in the two-Ioop approximation for two distinct gauge classes.

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Orientador: Marcos Benevenuto Jardim / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Educação / Made available in DSpace on 2018-08-23T02:27:37Z (GMT). No. of bitstreams: 1 Barbosa_RodrigodeMenezes_M.pdf: 1767185 bytes, checksum: abee129d89bf1e5149600bcac1bb76be (MD5) Previous issue date: 2013 / Resumo: Neste trabalho estudamos teorias de calibre em variedades de dimensão alta, com ênfase em variedades Calabi-Yau, G2 e Spin(7). Começamos desenvolvendo a teoria de conexões em fibrados e seus grupos de holonomia, culminando com o teorema de Berger que classifica as possíveis holonomias de variedades Riemannianas e o teorema de Wang relacionando a holonomia à existência de espinores paralelos. A seguir, descrevemos em mais detalhes as estruturas geométricas resultantes da redução da holonomia, incluindo aspectos topológicos (homologia e grupo fundamental) e geométricos (curvatura). No último capítulo desenvolvemos o formalismo de teoria de calibre em dimensão quatro: introduzimos o espaço de moduli de instantons e realizamos as reduções dimensionais das equações de anti-autodualidade. Com esta motivação procedemos a estudar teorias de calibre em variedades de holonomia especial e também algumas de suas reduções dimensionais / Abstract: In this work we study gauge theory on high dimensional manifolds with emphasis on Calabi-Yau, G2 and Spin(7) manifolds. We start by developing the theory of connections on fiber bundles and their associated holonomy groups, culminating with Berger's theorem classifying the holonomies of RIemannian manifolds and Wang's theorem relating the holonomy groups to the existence of parallel spinors. We proceed to describe in more detail the geometric structures resulting from holonomy reduction, including topological (homology and fundamental group) and geometric (curvature) aspects. In the last chapter we develop the formalism of gauge theory in dimension four: we introduce the moduli space of instantons and the dimensional reductions of the anti-selfduality equations. With this motivation in mind, we proceed to study gauge theories on manifolds of special holonomy and also some of their dimensional reductions / Mestrado / Matematica / Mestre em Matemática

A new method is developed for treating atoms and molecules in a magnetic field in a gauge-invariant way using the Rayleigh-Ritz energy variational principle. The energy operator depends on the vector potential which must be chosen in some gauge. In order to adapt the trial wave function to the gauge of the vector potential, the trial wave function can be multiplied by a phase factor which depends on the spatial coordinates. When the energy expectation value is minimized with respect to the phase function, the equation for charge conservation for stationary states is obtained. This equation can be solved for the phase function, and the solution used in the energy expectation value to obtain a gauge-invariant energy. The method is applicable to all quantum mechanical systems for which the variational principle can be applied. It ensures satisfaction of the charge conservation condition, a gauge-invariant energy, and the best upper bound to the ground-state energy which can be obtained for the form of trial wave function chosen.

A system of nonrelativistic charged particles and radiation is canonically quantized in the Coulomb gauge and Maxwell's equations in quantum electrodynamics are derived. By requiring form invariance of the Schrodinger equation under a space and time dependent unitary transformation, operator gauge transformations on the quantized electromagnetic potentials and state vectors are introduced. These gauge transformed potentials have the same form as gauge transformations in non-Abelian gauge field theories. A gauge-invariant method for solving the time-dependent Schrodinger equation in quantum electrodynamics is given. Maxwell's equations are written in a form which holds in all gauges and which has formal similarity to the equations of motion of non-Abelian gauge fields. A gauge-invariant derivation of conservation of energy in quantum electrodynamics is given. An operator gauge transformation is made to the multipolar gauge in which the potentials are expressed in terms of the electromagnetic fields. The multipolar Hamiltonian is shown to be the minimally coupled Hamiltonian with the electromagnetic potentials in the multipolar gauge. The model of a charged harmonic oscillator in a single-mode electromagnetic field is considered as an example. The gauge-invariant procedure for solving the time-dependent Schrodinger equation is used to obtain the gauge-invariant probabilities that the oscillator is in an energy eigenstate For comparison, the conventional approach is also used to solve the harmonic oscillator problem and is shown to give gauge-dependent amplitudes.