The Kirillov picture for the Wigner particle*In memory of E C G Sudarshan. (25th May 2018)

• Record Type: Journal Article
• Authors: Gracia-Bondía, J M; Lizzi, F; Várilly, J C; Vitale, P
• Is Part Of: Journal of physics. Volume 51:Number 25(2018)
• Publication Date: 2018-05-25
• Subjects: Wigner particle -- continuous spin -- coadjoint orbits; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aac3b3
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: 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.