Wigner–Souriau translations and Lorentz symmetry of chiral fermions

Christian Duval (1, 2) , M Elbistan (3) , P.A. Horváthy (4, 3) , P.-M Zhang (4)

1 CPT - E2 Géométrie, Physique et Symétries
2 CPT - Centre de Physique Théorique - UMR 7332
3 LMPT - Laboratoire de Mathématiques et Physique Théorique
4 INSTITUTE OF MODERN PHYSICS - Institute of Modern Physics

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 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;

Keywords: ELECTRON

Domains: High Energy Physics - Theory [hep-th]; High Energy Physics - Phenomenology [hep-ph]; Mathematical Physics [math-ph]

Christian Duval, M Elbistan, P.A. Horváthy, P.-M Zhang. Wigner–Souriau translations and Lorentz symmetry of chiral fermions. Physics Letters B, 2015, 742, pp.322-326. ⟨10.1016/j.physletb.2015.01.048⟩. ⟨hal-01218185⟩