Unified Field Theoretical Models from Generalized Affine Geometries II

DIEGO JULIO CIRILO

INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS

SPRINGER/PLENUM PUBLISHERS

Año: 2011 p. 1699 - 1708

0020-7748

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 R ⊗ O3 ∼ R ⊗ SU(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 YangMills 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.