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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/97533We 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.Latex, 5 pages, revtex, no figuresHigh Energy Physics - TheoryQuantization of the Particle Motion on the $n$-Dimensional Spheretext