Campos de Yang-Mills fracamente estáveis na esfera de dimensão quatro

• Autor(a) principal: Caetano Junior, Claudinei
• Data de Publicação: 2023
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFSCAR
• Texto Completo: https://repositorio.ufscar.br/handle/ufscar/18250
• topic: Teoria de Yang-Mills; Funcional de Yang-Mills; Campos de Yang-Mills; Teoria de calibre; Fibrados; Conexões; Derivada covariante; Yang-Mills theory; Yang-Mills functional; Yang-Mills fields; Gauge theory; Fiber bundles; Connections; Covariant derivative; CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA

In this work we made a quick study on some basic results related to Groups and Lie Algebras, action of Groups and Fiber Bundles with the objective of defining connections in Principal Bundles and, later, in Associated Vector Bundles. Once these concepts are understood, in the main part of this work, following the article Stability and Isolation Phenomena for Yang-Mills Fields by J.P. Bourguignon and H. B. Lawson Jr., we developed the “geometric environment” and defined the Yang-Mills Functional in order to demonstrate a stability result, namely: every weakly stable Yang-Mills field on S4 with structure group G = SU(2),SU(3),U(1) or U(2) is self-dual or anti-self-dual.