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.
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1987
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