Classical aspect of spin angular momentum in geometric quantum mechanics

Geometric Quantum Mechanics is a formulation demonstrating how quantum theory may be cast in the language of Hamiltonian phase-space dynamics.  Within this framework, the classical properties of spin $\frac{1}{2}$, spin 1 and spin $\frac{3}{2}$ particles have been studied.  The correspondence between the Poisson bracket and commutator algebras for these systems was shown by explicitly computing the value of the commutator of spin operators and comparing it with the Poisson bracket of the corresponding classical observables.  This study was extended by comparing the Casimir operator and its classical counterpart.  The results showed that there exists a correspondence between classical and quantum Casimir operators at least for the case of spin $\frac{1}{2}$.  This research clearly shows the limit of classical notions to describe the purely quantum concept.