Uma abordagem geométrica para princípios de localização de integrais funcionais

• Autor(a) principal: Dias, M. A [UNESP]
• Data de Publicação: 2007
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://hdl.handle.net/11449/138361; http://www.athena.biblioteca.unesp.br/exlibris/bd/cathedra/11-04-2016/000855888.pdf
• topic: Fisica matematica; Integração funcional; Mathematical physics

We present in this dissertation a conceptual review of differential geometry, where we are interested in defining vector fields which are one-parameter transformation generators, differential forms, symplectic manifolds, and fiber bundles. In addition, we detail the concept about De Rham's cohomology, which provides us a fundamental algebraic tool to analyze topological properties of manifolds. The combination of these concepts, which are the background material of our work, allows us to develop equivariant localization theories of integrals defined on classical phase spaces, which can also be a co-adjoint orbit. The localization is possible because of the Duistermaat-Heckman theorem, which allows us to write integrals on the whole space just as a sum, or integral, on a critical points set. Further more, we do an extension to functional integrals localization theories, where it is needed to define loop spaces. In this context we apply equivariant localization formulation having the bases of Atiyah-Witten conjecture to supersymmetric theories, where we derive the Atiyah-Singer index theorem for a Dirac operator. The index theorem is applied to chiral anomaly calculation