Abstract
It is shown that every Lorentz transformation can be decomposed into a helicity-preserving transformation that changes the momentum of a free particle and a helicity-changing transformation that leaves the momentum invariant. Since momentum-preserving transformations constitute a subgroup of the Lorentz group, helicity-preserving transformations form a coset space. It is shown further that, for massive particles, every Lorentz transformation can be decomposed into the Wigner rotation and helicity-preserving transformations. For massless particles, every Lorentz transformation can be decomposed into the gauge transformation and helicity-preserving transformation. The gauge transformation in this case is a Lorentz-boosted Wigner rotation.
Published Version
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