Spin

Summary

Spin is the intrinsic angular momentum of a quantum particle, carried in addition to the orbital angular momentum of its motion. A particle of spin $s$, with $s$ an integer or half-integer, has an internal state space of dimension $2s + 1$. Rotations act on it through an irreducible representation of SU(2). Half-integer spins, such as $\frac12$ for the electron, have no classical analogue: a rotation by $2\pi$ multiplies the state by $-1$. Spin decides the statistics of identical particles: particles of half-integer spin are fermions and those of integer spin are bosons.