Eulerian parametrization of Wigner’s little groups and gauge transformations in terms of rotations in two-component spinors

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Abstract
A set of rotations and Lorentz boosts is presented for studying the three‐parameter little groups of the Poincaré group. This set constitutes a Lorentz generalization of the Euler angles for the description of classical rigid bodies. The concept of Lorentz‐generalized Euler rotations is then extended to the parametrization of the E(2)‐like little group and the O(2,1)‐like little group for massless and imaginary‐mass particles, respectively. It is shown that the E(2)‐like little group for massless particles is a limiting case of the O(3)‐like or O(2,1)‐like little group. A detailed analysis is carried out for the two‐component SL(2,c) spinors. It is shown that the gauge degrees of freedom associated with the translationlike transformation of the E(2)‐like little group can be traced to the SL(2,c) spins that fail to align themselves to their respective momenta in the limit of large momentum and/or vanishing mass.