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The Kirillov picture for the Wigner particle. (English) Zbl 1395.81136

Summary: We discuss the Kirillov method for massless Wigner particles, usually (mis)named ‘continuous spin’ or ‘infinite spin’ particles. These appear in Wigner’s classification of the unitary representations of the Poincaré group, labelled by elements of the enveloping algebra of the Poincaré 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.

MSC:

81S10 Geometry and quantization, symplectic methods
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
81R25 Spinor and twistor methods applied to problems in quantum theory
17B08 Coadjoint orbits; nilpotent varieties
53D50 Geometric quantization
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References:

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