  One of the most satisfactory pictures for spinning particles is the
Barut-Zanghi (BZ) classical theory for the relativistic extended-like electron,
that relates spin to zitterbewegung (zbw). The BZ motion equations constituted
the starting point for recent works about spin and electron structure,
co-authored by us, which adopted the Clifford algebra language. This language
results to be actually suited and fruitful for a hydrodynamical re-formulation
of the BZ theory. Working out, in such a way, a ``probabilistic fluid'', we are
allowed to re-interpret the original classical spinors as quantum
wave-functions for the electron. Thus, we can pass to ``quantize" the BZ theory
employing this time the tensorial language, more popular in first-quantization.
``Quantizing'' the BZ theory, however, does not lead to the Dirac equation, but
rather to a non-linear, Dirac--like equation, which can be regarded as the
actual ``quantum limit'' of the BZ classical theory. Moreover, an original
variational approach to the the BZ probabilistic fluid shows that it is a
typical ``Weyssenhoff fluid'', while the Hamilton-Jacobi equation (linking
together mass, spin and zbw frequency) appears to be nothing but a special case
of de Broglie's famous energy-frequency relation. Finally, after having
discussed the remarkable correlation between the gauge transformation U(1) and
a general rotation on the spin plan, we clarify and comment on the
two-valuedness nature of the fermionic wave-function, and on the parity and
charge conjugation transformations.
