  This manuscript is devoted to introduce a gauge theory of the Lorentz Group
based on the ambiguity emerging in dealing with isometric
diffeo-morphism-induced Lorentz transformations. The behaviors under local
transformations of fermion fields and spin connections (assumed to be ordinary
world vectors) are analyzed in flat space-time and the role of the torsion
field, within the generalization to curved space-time, is briefly discussed.
The fermion dynamics is then analyzed including the new gauge fields and
assuming time-gauge. Stationary solutions of the problem are also analyzed in
the non-relativistic limit, to study the spinor structure of an hydrogen-like
atom.
