Wigner-Souriau translations and Lorentz symmetry of chiral fermions

Understand

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.