Operador de Dirac, espaços de Riemann- Cartan-Weyl e a natureza do campo gravitacional

AUTOR(ES)
DATA DE PUBLICAÇÃO

1992

RESUMO

In this work we present a formulation of Einstein s gravitational theory as a field theory in the sense of Faraday, i.e., as a theory in which the gravitational field, like the others physical fields, is defined on the flat Minkowski space-time. The main motivation for the construction of this theory comes from the fact that in the General Relativity does not exist genuine conservation laws for energy, momentum and angular momentum for the system composed by the gravitational field and the other physical fields. In order to formulate our theory, we develop new mathematical methods, which we callthe Clifford bundle formalism. In particular, we introduce the fundamental Dirac operator of a Riemann-Cartan-Weyl space-time and the associated Dirac operators, which play an important role in the theory. We observe that the introduction of the Dirac operators for Riemann-Cartan-Weyl spaces presented in this thesis is a novelty and for the best of our knowledge we never saw this operators being used previously in the literature. Several other operators, like the Dirac commutator and anticommutator, the Ricci and the Einstein operators, which do not have analogous in the formulation of the differential geometry à la Cartan, also appear here by the first time. Our formulation clarify many results presented in other attempts to formulate the gravitational theory in the Minkowski space-time and it suggests several possible generalizations of Einstein s theory. We believe that the theory presented in this thesis puts some light on both the physical and mathematical nature of the gravitational field

ASSUNTO(S)

relatividade (fisica) gravitação

ACESSO AO ARTIGO

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