Abstract
This communication is to be considered as an addendum to the reference (1). The purpose of that paper was to investigate, within the framework of geometric quantization à la Kostant — Souriau, the new notion of polarizer of a prequantizable symplectic manifold. Although that work was mainly concerned with the general scheme of compact semi-simple Lie groups, its ultimate motivation was clearly of physical nature. That is why it was there proposed to examine polarizers; a drastic selection of prequantizable coadjoint orbits showed up, which, in fact, might correspond to the actual selection of physically relevant multiplets of hadron spectroscopy. The question then arises: must one take polarizers seriously? In order to strenghthen our point of view, we propose here to discuss the properties of polarizers for spinning particles. The non relativistic Dirac particle, its Poincaré invariant polarizer is explicitely worked out, as well as for the spin 1 relativistic massive particle. The associated mixed (real + Kähler) polarization naturally corresponds to the unique Poincaré invariant polarization discovered by Souriau and Renouard.
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References
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© 1983 D. Reidel Publishing Company
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Duval, C. (1983). The Spin Polarizer. In: Cahen, M., De Wilde, M., Lemaire, L., Vanhecke, L. (eds) Differential Geometry and Mathematical Physics. Mathematical Physics Studies, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7022-9_12
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DOI: https://doi.org/10.1007/978-94-009-7022-9_12
Publisher Name: Springer, Dordrecht
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