In quantum mechanics, a particle in a box has discrete energy levels, while a particle in infinite space has a continuum of energy levels. The discreteness comes from the “compactness” of the box. Can we use this idea to explain why spin is quantized? Yes! The “box” in this case, however, is the group SU(2)!

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

2010.11.29 Monday ACHK