Quantization of the Particle Motion on the $n$-Dimensional Sphere

Petre Diţă

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arXiv · hep-th/9704207

Quantization of the Particle Motion on the $n$-Dimensional Sphere

Petre Diţă

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Abstract

We develop here a simple formalism that converts the second-class constraints into first-class ones for a particle moving on the $n$-dimensional sphere. The Poisson algebra generated by the Hamiltonian and the constraints closes and by quantization transforms into a Lie algebra. The observable of the theory is given by the Casimir operator of this algebra and coincides with the square of the angular momentum.

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Petre Diţă. 1997-04-30. Quantization of the Particle Motion on the $n$-Dimensional Sphere. https://arxiv.org/abs/hep-th/9704207

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