Covariant inertial forces for spinors

Abstract In this paper we consider the Dirac spinor field in interaction with a background of electrodynamics and torsion-gravity; by performing the polar reduction we acquire the possibility to introduce a new set of objects that have the geometrical status of non-vanishing tensors but which seem to contain the same information of the connection: thus they appear to be describing something that seems like an inertial force but which is also essentially covariant. After a general introduction, we exemplify these tensors in the very well known instance of the orbital of minimal energy for an electron in the case of the Hydrogen atom: we will see that the invariants built with these tensors remain different from zero even for free field configurations. An outlook regarding possible interpretations of such a set of tensors will be sketched. A few final comments will eventually be given