We present here a field theory of the spinning electron, by writing do
wn a new equation for the four-velocity field nu(mu) (different from D
irac theory), which allows a classically intelligible description of t
he electron. Moreover, we make explicit the kinematical properties of
such a velocity field (which are also different from the ordinary ones
). Finally, we analyze the internal zitterbewegung (zbw) motions, for
both time-like and space-like speeds. We adopt in this paper the ordin
ary tensorial language. Our starting point is the Barut-Zanghi classic
al theory for the relativistic electron, which relates spin with zbw.