PROPER DIRAC QUANTIZATION OF A FREE PARTICLE ON A D-DIMENSIONAL SPHERE

We show that an unambiguous and correct quantization of the second-cla ss constrained system of a free particle on a sphere in D dimensions i s possible only by converting the constraints to Abelian gauge constra ints, which are of first class in Dirac's classification scheme. The e nergy spectrum is equal to that of a pure Laplace-Beltrami operator wi th no additional constant arising from the curvature of the sphere. A quantization of Dirac's modified Poisson brackets for second-class con straints is also possible and unique, but must be rejected since the r esulting energy spectrum is physically incorrect. (C) 1997 Published b y Elsevier Science B.V.