 Little group

The little group of a fixed four-momentum $p$ is its stabilizer subgroup in the Lorentz group: $G_p=\{\Lambda :\Lambda p=p\}$. It changes internal states while leaving that momentum unchanged. In four spacetime dimensions, a massive rest momentum has spatial rotations as its little group; the corresponding Spin group is SU(2), permitting half-integer spin. A nonzero future-directed massless four-momentum instead has the planar Euclidean little-group structure. Its finite-helicity quantum states have trivial translation action. These group representations, combined with the momentum orbit, underlie Wigner's classification.^[ref]