  Chiral fermions can be embedded into Souriau's massless spinning particle
model by "enslaving" the spin, viewed as a gauge constraint. The latter is not
invariant under Lorentz boosts; spin enslavement can be restored, however, by a
subsequent Wigner-Souriau (WS) translation, analogous to a compensating gauge
transformation. The combined transformation is precisely the recently uncovered
twisted boost, which we now extend to finite transformations. WS-translations
are identified with the stability group of a motion acting on the right on the
Poincare group, whereas the natural Poincare action corresponds to action on
the left. The relation to non-commutative mechanics is explained.
