MG13 - Talk detail

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Geometrical analysis of a new type of Unified Field Theoretical models following the guidelines of previous works of the author is presented. These unified models are characterized by an underlying hypercomplex structure, zero non-metricity and their geometrical action is determined essentially by the curvature provenient from the symmetry breaking of a group manifold in higher dimensions. The mechanism of Cartan-MacDowell-Mansouri type, allows us to construct geometrical actions of determinantal type, leading to a non topological physical Lagrangian due to the splitting of a reductive geometry. Our goal is to take advantage of the geometrical and topological properties of this theory in order to determine the minimal group structure of the resultant spacetime Manifold requiered to support a fermionic structure. From this fact, the relation between antisymmetric torsion and Dirac structure of the spacetime is determined, and the existence of an important contribution of the torsion to the gyromagnetic factor of the fermions, shown. Also, we resume and analyze previous cosmological solutions in this new UFT where, as in our work [Class. Quantum Grav.22 (2005) 4987–5004] for the non abelian Born-Infeld model, the Hosoya-Ogura ansatz is introduced for the important cases of tratorial, totally antisymmetric and general torsion fields. In the case of spacetimes with torsion, the real meaning of the spin-frame alignment is find and the question of the minimal coupling is discussed.

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