Transformações conformes

• Ano de defesa: 2018
• Autor(a) principal: Sidiney Bruno Montanhano
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Brasil; Departamento de Matemática; Programa de Pós-Graduação em Matemática; UEM; Maringá, PR; Centro de Ciências Exatas
• Palavras-chave em Português: Transformações conformes, Grupo ortogonal generalizado, Álgebra de Witt, Álgebra de Virasoro, Quantização,; Conformal transformations, Generalized orthogonal group, Witt algebra, Virasoro algebra, Quantization; Ciências Exatas e da Terra; Matemática
• Link de acesso: http://repositorio.uem.br:8080/jspui/handle/1/5518

This work presents a study of conformal transformations, more specifically the case of semi-Riemannian flat spaces, like Euclidean and Minkowskian spaces. This study is made with an exposition of the relations of the conformal transformations with the generalized orthogonal transformations. Having these relationships, we identify the properties of these transformations, and their Lie groups. Focusing on the two-dimensional case, we identify the Witt algebra and its unique non-trivial one-dimensional central extension, the Virasoro algebra, as personifications of conformal transformations, and thus we do a study of these algebras and their representations. In addition, throughout the work we show physical applications, like the quantization, and how conformal transformations behave in those applications. Finally, we introduce bosonic string theory as a physical as well as a mathematical application of the subject of this work