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Quantizing compact phase spaces: Irreducible representations from constrained dynamics

par Gates, Evalyn;Potting, Robertus ;Taylor, Cyrus;Velikson, Boris
Référence Physical review letters, 63, 24, page (2617-2620)
Publication Publié, 1989

Article révisé par les pairs

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Résumé :

We study the quantization of the coset space SU(3)/U(1)×U(1), considered as an example of a compact phase space. We embed this system in the flat space C6 endowed with a Poisson-bracket structure, then quantize it as a constrained system, finding consistency only for isolated symplectic structures. The space of states for each admissible symplectic structure forms an irreducible representation of SU(3). In this way, we recover in the language of constrained dynamics some of the results of the Borel-Weil-Bott theorem and geometric quantization. © 1989 The American Physical Society.