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arXiv · 1411.6541

Wigner-Souriau translations and Lorentz symmetry of chiral fermions

C. Duval·M. Elbistan·P. A. Horvathy·P. -M. Zhang
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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.

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C. Duval, M. Elbistan, P. A. Horvathy, P. -M. Zhang. 2015-01-18. Wigner-Souriau translations and Lorentz symmetry of chiral fermions. https://doi.org/10.1016/j.physletb.2015.01.048

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