Abstract
We study the free motion of a particle on a sphere SN −1, at both the classical and the quantum level. Particular attention is paid to such aspects as ground state degeneracy, orbit space, orthogonal symmetry and its quantum implementation, superintegrability, Casimir operators, spectrum-generating groups, as well as supersymmetric solutions and extensions, all with a view to obtaining a better understanding of the field-theoretic sigma models.
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