Wigner-Souriau translations and Lorentz symmetry of chiral fermions
arXiv:1411.6541 · doi:10.1016/j.physletb.2015.01.048
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.
v3: a new Section explaining the relation to non-commutativity is added. 14 pages, 2 figures