"Dirac equation in space-time with torsion": improvements and further comments

The derivation of Dirac equation previously studied in a curved space-time with torsion is reconsidered. As in the original paper the total action, sum of the Einstein Hilbert Cartan and of the Dirac action, is considered. The Dirac equation fallows, with improvements, by varying with respect to the Dirac spinor and to the torsion field, Variation with respect to the gravitational field is not considered. The equation is translated into the language of the 2 spinor formalism of Newman and Penrose with many improvement and clarifications. Contrarily to the original result, here there are at least two possible forms of the final equation. Both form have the same torsion dependent part. Instead the torsion free part in one case leads to Chandrasekhar like formulation (as in the original paper), while in the other case to the Penrose - Rindler's one. The torsion induced non linearity is represented by the interaction of the particle with its own current that remains conserved.