International audienceChiral 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 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 isometries of an exact plane gravitational wave are symmetries for both massive and massless particles. Their conformal extensions which are in fact Chrono-Projective transformations introduced by Duval et al are symmetries for massless particles and play an important role for the Memory Effect. The generically 5-parameter isometry group extends under special circumstances to a 6 parameter group, further extended by homotheties, which are universal Chrono-Projective symmetries for any profile.