GENERALIZED AFFINE GEOMETRIES, STRUCTURE OF SPACETIME AND UNIFICATION

DIEGO JULIO CIRILO

EINSTEIN AND OTHERS: Unification

NOVA SCIENCE PUBLISHERS

Año: 2015; p. 39 - 72

Geometrical analysis of a new type of the Unified Field Theoretical models followingthe guidelines of previous works of the author is presented. These unified modelsare characterized by an underlying hypercomplex structure, zero non-metricity andtheir geometrical action which is determined essentially by the curvature provenientfrom the symmetry breaking of a group manifold in higher dimensions. The mechanismof Cartan-MacDowell-Mansouri type, allows us to construct geometrical actionsof the determinantal type, leading to a non topological physical Lagrangian due to thesplitting of a reductive geometry. Our goal is to take advantage of the geometrical andtopological properties of this theory in order to determine the minimal group structureof the resultant spacetime Manifold requiered to support a fermionic structure. Fromthis fact, the relation between the antisymmetric torsion and the Dirac structure of thespacetime is determined, and the existence of an important contribution of the torsionto the gyromagnetic factor of the fermions, shown. Also, we resume and analyze previouscosmological solutions in this new UFT where, as in our work [Class. QuantumGrav.22 (2005) 4987?5004] for the non abelian Born-Infeld model, the Hosoya-Oguraansatz is introduced for the important cases of tratorial, totally antisymmetric and generaltorsion fields. In the case of spacetimes with torsion, the real meaning of thespin-frame alignment is found and the question of the minimal coupling is discussed.