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The problem of quantizing a particle on a 2-sphere has been treated by numerous approaches, including Isham's global method based on unitary representations of a symplectic symmetry group that acts transitively on the phase space.
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J. Guerrero, F. F. López-Ruiz, and V. Aldaya, “ S U ( 2 ) SU(2) -particle sigma model: momentum-space quantization of a particle on the sphere S 3 S^{3} ,” Journal of Physics A: Mathematical and Theoretical
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