Proper Dirac Quantization of Free Particle on D-Dimensional Sphere

Abstract

We show that an unambiguous and correct quantization of the second-class constrained system of a free particle on a sphere in $D$ dimensions is possible only by converting the constraints to abelian gauge constraints, which are of first class in Dirac's classification scheme. The energy spectrum is equal to that of a pure Laplace-Beltrami operator with no additional constant arising from the curvature of the sphere. A quantization of Dirac's modified Poisson brackets for second-class constraints is also possible and unique, but must be rejected since the resulting energy spectrum is physically incorrect.

Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html Paper also at http://www.physik.fu-berlin.de/~kleinert/kleiner_re253/preprint.html

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