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Proper Dirac Quantization of Free Particle on D-Dimensional Sphere

Hagen Kleinert·Sergei V. Shabanov
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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.

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Hagen Kleinert, Sergei V. Shabanov. 1997-02-01. Proper Dirac Quantization of Free Particle on D-Dimensional Sphere. https://doi.org/10.1016/s0375-9601(97)00410-6

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