Métodos da teoria de calibre na gravitação newtoniana
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Data
2023-03-30
Autores
Lima, Matheus dos Santos
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Universidade Federal do Espírito Santo
Resumo
Élie Cartan developed the concept of affine connection as a way to establish a local equivalence relation between sections of the tangent space to four-dimensional spacetime. This concept allowed for an intrinsic description of local geometric properties, independent of an external coordinate system. By adopting the method of moving frames, Cartan provided a precise geometric description of spacetime, enriching our understanding of the theory of general relativity. This dissertation aims to study Cartan’s works and highlight his contributions, through the affine connection, to the geometrization of the Newtonian physical system, as well as to identify possible connections with contemporary Gauge Theory, which offers a powerful framework for describing fundamental interactions of this nature. In this context, the main objective of this study is to propose equations that allow for finding an affine connection that is a Yang-Mills connection modeling the physical phenomena under study. By seeking this connection between Cartan’s theory and Gauge Theory, we aim to advance our understanding of fundamental interactions and possibly pave the way for future work.
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Conexão afim , Sistema físico newtoniano , Teoria de Calibre , Conexão de Yang-Mills