The physical meaning of the particularly simple non-degenerate supermetric, introduced in the previous part by the authors, is elucidated and the possible connection with processes of topological origin in high energy physics is analyzed and discussed. New possible mechanism of the localization of the fields in a particular sector of the supermanifold is proposed and the similarity and differences with a 5-dimensional warped model are shown. The relation with gauge theories of supergravity based in the OSP (1/4) group is explicitly given and the possible original action is presented. We also show that in this non-degenerate super-model the physic states, in contrast with the basic states, are observables and can be interpreted as tomographic projections or generalized representations of operators belonging to the metaplectic group M p (2) .The advantage of geometrical formulations based on non-degenerate super-manifolds over degenerate ones is pointed out and the description and the analysis of some interesting aspects of the simplest Riemannian superspaces are presented from the point of view of the possible vacuum solutions .

New model of a non-dualistic Unified Theory is analyzed. This model is based in a manifold equipped with an underlying hypercomplex structure and zero non-metricity, that makes it geometricaly and physically consistent. Wormhole solution from this new model is presented and is explicitly compared with our previous one coming from the EinsteinNon Abelian Born-Infeld theory (in Class. Quantum Gravity 22: [4987][4988][4989][4990][4991][4992][4993][4994][4995][4996][4997][4998][4999][5000][5001][5002][5003][5004] 2005). We find that the torsion plays in this unified theory similar role that Yang Mills type strength field coming from the non-Abelian Born-Infeld energy momentum tensor. The meaning of the Yang-Mills ansatz based in the alignment of the isospin with the frame geometry of the spacetime is discussed.

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A new metric is obtained by applying a complex coordinate transformation to the static metric of the self-gravitating Born–Infeld monopole. The behaviour of the new metric is typical of a rotating charged source, but this source is not a spherically symmetric Born–Infeld monopole with rotation. We show that the structure of the energy–momentum tensor obtained with this new metric does not correspond to the typical structure of the energy–momentum tensor of Einstein–Born–Infeld theory induced by a rotating spherically symmetric source. This also shows that the complex coordinate transformations have the interpretation given by Newman and Janis only in spacetime solutions with linear sources.

The space-time structure of the new Unified Field Theory presented in previous reference (Int. J. Theor. Phys. 49:1288-1301, 2010 is analyzed from its SL(2C) underlying structure in order to make precise the notion of minimal coupling. To this end, the framework is the language of tensors and particularly differential forms and the condition a priory of the existence of a potential for the torsion is relaxed. We shown trough exact cosmological solutions from this model, where the geometry is Euclidean (2), the relation between the space-time geometry and the structure of the gauge group. Precisely this relation is directly connected with the relation of the spin and torsion fields. The solution of this model is explicitly compared with our previous ones and we find that: (i) the torsion is not identified directly with the Yang Mills type strength field, (ii) there exists a compatibility condition connected with the identification of the gauge group with the geometric structure of the space-time: this fact lead the identification between derivatives of the scale factor a(τ ) with the components of the torsion in order to allows the Hosoya-Ogura ansatz (namely, the alignment of the isospin with the frame geometry of the space-time), (iii) this compatibility condition precisely mark the fact that local gauge covariance, coordinate independence and arbitrary space time geometries are harmonious concepts and (iv) of two possible structures of the torsion the "tratorial" form (the only one studied here) forbids wormhole configurations, leading only, cosmological instanton space-time in eternal expansion.

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In this work the underlying structure of new type of Unified Field Theoretical model introduced in by the authors is elucidated and analyzed from the geometrical and group theoretical point of view. 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 able to support a fermionic structure. From this fact, the relation between antisymmetric torsion and Dirac structure of the spacetime is determined and important physical consequences enumerated. In the case of spacetime with torsion the real meaning of the spin-frame alignment is find and the question of the minimal coupling is discussed based in the important cases of tratorial, totally antisymmetric and general torsion fields. Motivation and Summary of the ResultsAs was pointed out by us in later works [1,2], the cornerstone of the problem of the Unification is where to start conceptually to reformulate the theoretical arena where the Fundamental Theory will be placed, and where the geometry is the unifying essence. According to Mach spacetime doesn't exists without matter. Then, two basic ideas immediately arise to fulfill the observation given by Mach: the concept of dualistic or non-dualistic theories. In the first one the simplest and economical description can be formulated in terms of the gravitational field without torsion plus the energy momentum tensor that, however, is added "by hand" in order to cover the lack of knowledgement of a fundamental structure of the space

Non-Riemannian generalization of the standard Born-Infeld (BI) Lagrangian is introduced and analized from a theory of gravitation with dynamical torsion field. The field equations derived from the proposed action lead to a trace free gravitational equation (non-riemannian analog to the trace free equation (TFE) from[1][2][3]) and the field equations for the torsion respectively.In this theoretical context, the fundamental constants arise all from the same geometry through geometrical invariant quantities (as from the curvature R). New results involving generation of primordial magnetic fields and the link with leptogenesis and baryogenesis are presented and possible explanations given. The physically admisible matter fields can be introduced in the model via the torsion vector h µ . Such fields include some dark matter candidates such as axion, right neutrinos and Majorana and moreover, physical observables as vorticity can be included in the same way. From a new wormhole soluton in a cosmological spacetime with torsion we also show that the primordial cosmic magnetic fields can originate from h µ with the axion field (that is contained in h µ ) the responsible to control the dynamics and stability of the cosmic magnetic field but not the magnetogenesis itself. The analisys of Grand Unified Theories (GUT) in the context of this model indicates that the group manifold candidates are based in SO(10), SU (5) or some exceptional groups as E(6),E (7), etc. Contents