  Spinor fields are considered in a generally covariant environment where they
can be written in the polar form. The polar form is the one in which spinorial
fields are expressed as a module times the exponential of a complex
pseudo-phase, and in this form the full spinorial field theory can in turn be
expressed by employing only real tensorial quantities. Such a reformulation
makes it possible to emphasize properties of the spinorial field theory, and
this would enrich our understanding in ways that have never been followed up
until this moment.
