Asymptotic Quantization of a Particle on a Sphere

Quantum systems whose states are tightly distributed among several invariant subspaces (variable spin systems) can be described in terms of distributions a four-dimensional phase-space T∗S2 the limit large average angular momentum. The cotangent bundle is also classical manifold for with E(3) symmetry group appropriately fixed Casimir operators. This allows us to employ asymptotic form star-product proper variable (integer) develop deformation quantization scheme particle moving on two-dimensional sphere, observables elements e(3) algebra and corresponding T∗S2. We show that standard commutation relations recovered from Poisson brackets explicit expressions eigenvalues eigenfunctions some quantized (such as momentum operators their squares) obtained.