Wigner’s little group and decomposition of Lorentz transformations

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Abstract
It is shown how an arbitrary Lorentz transformation can be expressed in terms of elements of Wigner’s little group and its cosets. This yields a natural parametrization for the little group, while its coset members turn out to be helicity-preserving transformations. The associated Wigner angle and its relation to the actual change in helicity are discussed. Finally, the extension to zero-mass particles shows how the little group becomes a gauge transformation in that limit.