Helicity (particle physics)

It is also rotationally invariant, in that a rotation applied to the system leaves the helicity unchanged.

In this sense, helicity can be contrasted to chirality, which is Lorentz invariant, but is not a constant of motion for massive particles.

[citation needed] For massless particles, the two coincide: The helicity is equal to the chirality, both are Lorentz invariant, and both are constants of motion.

By contrast, for massive particles, distinct chirality states (e.g., as occur in the weak interaction charges) have both positive and negative helicity components, in ratios proportional to the mass of the particle.

In d + 1 dimensions, the little group is the double cover of SE(d − 1) (the case where d ≤ 2 is more complicated because of anyons, etc.).