Spinor fields on the bulk and on compactified dimensions

This work has as the main aim to explore the nature of the fermionic fields, through a classification of spinor fields about physical space of interest, such as the bulk and the compactified space $S^7$ from the supergravity theories. This classification has an extreme utility in the exploration and in the search for new type of particles, whose observables correspond to bilinear covariants. In this way, these fields are classified into classes, through constraints obtained by means of the Fierz-Pauli-Kofink identities and the bilinear symmetries. We found the Lagrangian terms for the free spinor fields on spaces of seven compactified dimension in supergravity and, as application of our spinor fields classification on the bulk, we associate the invariants on axisymmetric black holes to the components of the bilinear covariants of the correspondent fermionic field. Besides, we found that a type of spinor denominated flag-dipole does not generate a brane, but degenerate itself in other type of spinor called dipole and, in compactification theories, we obtained the expression to the quantum field on compactified spaces for low energies in terms of creation and annihilation operators.