Fases Geométricas e suas relações com a Teoria de Fibrados e Representação de Grupos.

We present the own mathematic formalism to, first of all, study the holonomy interpretations of the adiabatic geometric phase presented by Berry-Simon and Aharanov-Anadan and, after this, the similirities found with the theory of representation groups, particularly, with the Borel-Weil-Bott theorem....

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Detalles Bibliográficos
Autor: Carvalho Neto, Osvaldo Fernandes
Tipo de recurso: tesis de maestría
Estado:Versión publicada
Fecha de publicación:2008
País:Brasil
Institución:Universidade Federal da Paraíba (UFPB)
Repositorio:Biblioteca Digital de Teses e Dissertações da UFPB
Idioma:portugués
OAI Identifier:oai:repositorio.ufpb.br:tede/7394
Acceso en línea:https://repositorio.ufpb.br/jspui/handle/tede/7394
Access Level:acceso abierto
Palabra clave:Matemática
Fibrado linha
Holonomia
Berry s phase
Adiabatic phase
Line Bundle
Homolonomy
Nonadiabatic phase
CIENCIAS EXATAS E DA TERRA::MATEMATICA
Descripción
Sumario:We present the own mathematic formalism to, first of all, study the holonomy interpretations of the adiabatic geometric phase presented by Berry-Simon and Aharanov-Anadan and, after this, the similirities found with the theory of representation groups, particularly, with the Borel-Weil-Bott theorem. These relations are made through classification of complex bundle line, and these results are used to introduce a cranked Hamiltonian. In general, we also show that the parameter space is a flag manifold or a submanifold of her and present a topologic argument of this space that indicates the relation between the structure Riemannian and the Berry s connection.