We discuss the Kirillov method for massless Wigner particles, usually (mis)named continuous spin or infinite spin particles. These appear in Wigners classification of the unitary representations of the Poincare group, labelled by elements of the enveloping algebra of the Poincare Lie algebra. Now, the coadjoint orbit procedure introduced by Kirillov is a prelude to quantization. Here we exhibit for those particles the classical Casimir functions on phase space, in parallel to quantum representation theory. A good set of position coordinates are identified on the coadjoint orbits of the Wigner particles; the stabilizer subgroups and the symplectic structures of these orbits are also described.
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