On unified field theories, dynamical torsion and geometrical models

A new model of a nondualistic unified theory is proposed. This model is absolutely consistent from the mathematical and geometrical points of view and is based on a manifold equipped with an underlying hypercomplex structure and zero nonmetricity. Also we showed that interesting wormhole solutions, similar to the non-Abelian Born-Infeld theory of our previous work [14] can be obtained. The solution of this model is explicitly compared with our previous one and we find that the torsion plays in this unified theory a role similar to that of Yang-Mills type strength field coming from the non-Abelian Born-Infeld energy momentum tensor. The meaning of the Hosoya-Ogura ansatz (namely, the alignment of the isospin with the frame geometry of the space-time) is completely elucidated.