Abstract
<p>These lecture notes were meant to compile the main ideas on gauge field theory and modern cosmology, showing the recent contributions of the author in these areas, including classical thermodynamics, supergravity and quantum gravity. Although the author has conducted the work without wishing to exhaust the issues in question, this synthesis provides some essential formal approaches for further studies, with relevant and updated references, as well as indications of classical readings. Special attention was given to the application of Lyra's geometry, because of its growing importance in quantum cosmology, and to the so-called &lt;&lt;paleogravity&gt;&gt;, a model of supergravity developed by the author with the purpose to offer a classical representation for supergravity that could be made compatible with the quantum theory of spacetime also developed by himself. Also in general cosmology, the emphasis was on inhomogeneous models due to the debate they open on the validity of the standard model. In this sense, the author presented his perturbative formalism of weak gravitational lensing by defining an inhomogeneous cosmological refractive index within a Lemaître-Tolman universe. Lastly, some remarks on Stephani cosmology were organized in order to expose the most significant features of this approach. During the reading, it shall be possible to observe some title marks indicating items of interest, as well as small side texts with outgivings of renowned authors.</p><p><strong>Key words</strong><span>: gauge field theory, cosmology, Lyra's geometry, quantum gravity, supergravity.</span></p><p><span>======================================================================================================</span> </p><p>A presente coletânea de notas de aula foi organizada como compilação das principais idéias sobre teoria de campo de calibre e cosmologia moderna, mostrando as recentes contribuições do autor nessas áreas, incluindo termodinâmica clássica aplicada, supergravidade e gravitação quântica. Embora o trabalho tenha sido conduzido sem pretensões a esgotar os temas em apreço, a síntese produzida trata formalmente alguns aspectos essenciais para estudos posteriores, com referências relevantes e atualizadas, bem como indicações de leituras clássicas. Especial atenção foi dada à aplicação da geometria de Lyra, por sua crescente importância na cosmologia quântica, e à chamada &lt;&lt; paleogravidade &gt;&gt;, um modelo de supergravidade desenvolvido pelo autor com o propósito de oferecer uma representação clássica da supergravidade, o qual seria compatível com a teoria quântica do espaço-tempo também desenvolvida pelo autor. Em cosmologia geral, foi dada ênfase em modelos não-homogêneos devido ao amplo debate que eles abrem sobre a validade do modelo padrão. Nesse sentido, o autor apresentou seu formalismo perturbativo de lentes gravitacionais fracas, definindo um índice de refração cosmológico inomogêneo dentro de um universo de Lemaître-Tolman. Por fim, algumas observações sobre a cosmologia de Stephani foram organizadas para expor as características mais significativas dessa abordagem. Durante a leitura, será possível observar algumas marcas indicativas de itens de interesse, bem como pequenos textos marginais com comentários de autores renomados.</p><p><strong>Palavras-chave</strong>: teoria de gauge, cosmologia, geometria de Lyra, gravidade quântica, supergravidade.</p><div><span style="font-size: 14px;"><br /></span></div>
Highlights
These lecture notes were meant to compile the main ideas on gauge eld theory and modern cosmology, showing the recent contributions of the author in these areas, especially in classical thermodynamics, supergravity and quantum gravity
Special attention was given to author's application of Lyra's geometry, because of its growing importance in quantum cosmology, and to the so-called paleogravity, a model of supergravity developed by the author with the purpose to oer a classical representation for supergravity that could be made compatible with the quantum theory of spacetime developed by himself
[28] O'Raifeartaigh says that the fundamental idea contained in the gauge symmetry is that if a system remains invariant under a rigid group of continuous transformations, it remains invariant if the group is taken locally
Summary
In his beautiful book The Dawning of Gauge Theory [28] O'Raifeartaigh says that the fundamental idea contained in the gauge symmetry is that if a system remains invariant under a rigid group of continuous transformations (independent of spacetime), it remains invariant if the group is taken locally (depending on spacetime). Having in mind Lagrangian formalism, we want theories where the Lagrangian density is invariant under internal symmetry transformations that depend on the point in spacetime If such symmetry implies a dynamic, i.e., a natural description of the appropriate interactions of the theory, there is a signicant gain to the understanding of the physics running in the system under consideration. The application of the gauge principle consists in the introduction of new elds in the Lagrangian to remove the terms of symmetry breaking of this Lagrangian. This profound principle, which the hard history dates back to the twenties and thirties of the twentieth century, is applied to both quantum and classical situations, being in full compliance with general relativity (GR). A good reference is the old book of Narlikar and Padmanabhan [26], containing a complete presentation of the gauge principle
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