Wigner-Souriau translations and Lorentz symmetry of chiral fermions

TL;DR

This paper explores how Wigner-Souriau translations restore Lorentz invariance in chiral fermions modeled as massless spinning particles, revealing their connection to twisted boosts and non-commutative mechanics.

Contribution

It extends the understanding of Lorentz symmetry in chiral fermions by linking Wigner-Souriau translations to twisted boosts and their role in non-commutative mechanics.

Findings

Wigner-Souriau translations restore Lorentz invariance in chiral fermion models.

Twisted boosts are identified as combined transformations involving WS-translations.

The relation between WS-translations and non-commutative mechanics is clarified.

Abstract

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.