So the quantum-theoretic study of spin is pretty much the same as the study of an abstract free particle moving around on S^3, satisfying Schroedinger’s equation. The energy levels of this abstract particle correspond to the spin of the rotating body.
Geometrically, SU(2) is the same as what we mathematicians call S^3, or the 3-sphere – which is the unit sphere in R^4.
— Spin and the Harmonic Oscillator, John Baez
2010.01.17 Wednesday ACHK