Helicity (particle physics)

In physics, helicity is the projection of the spin onto the direction of momentum.

Overview

The angular momentum J is the sum of an orbital angular momentum L and a spin S. The relationship between orbital angular momentum L, the position operator r and the linear momentum (orbit part) p is

${\displaystyle \mathbf {L} =\mathbf {r} \times \mathbf {p} }$

so L's component in the direction of p is zero. Thus, helicity is just the projection of the spin onto the direction of linear momentum. The helicity of a particle is positive (" right-handed") if the direction of its spin is the same as the direction of its motion and negative ("left-handed") if opposite.

Helicity is

In this sense, helicity can be contrasted[2] to chirality, which is Lorentz invariant, but is not a constant of motion for massive particles. For massless particles, the two coincide: The helicity is equal to the chirality, both are Lorentz invariant, and both are constants of motion.

In

All known

A treatment of the helicity of gravitational waves can be found in Weinberg.[5] In summary, they come in only two forms: +2 and −2, while the +1, 0 and −1 helicities are "non-dynamical" (they can be removed by a gauge transformation).

Little group

In 3 + 1 dimensions, the

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.). As before, there are unitary representations which don't transform under the SE(d − 1) "translations" (the "standard" representations) and "continuous spin" representations.

See also

• Chirality (physics)
• Helicity basis
• Gyroball, a macroscopic object (specifically a baseball) exhibiting an analogous phenomenon
• Wigner's classification
• Pauli–Lubanski pseudovector

References

Other sources