# Helicity

## Why is it interesting?

Helicity is an important experimental observable, which describes the projection of the spin onto the direction of the momentum. Moreover, there is a close connection to the more fundamental concept chirality, because for massless particles the chirality and helicity are the same.

Important Related Concepts:

## Layman

Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party.

## Student

Whether spin, helicity or chirality is important depends on the physical question you are interested in. For free massless spinors, the spin eigenstates are also helicity eigenstates and chirality eigenstates. In other words, the Hamiltonian for the massless Dirac equation commutes with the operators for chirality, γ5, helicity, S⃗·p⃗, and the spin operators, S⃗. The E QED interaction ψ ̄A/ψ = ψ ̄LA/ψL + ψ ̄RA/ψR is non-chiral, that is, it preserves chirality. Helicity, on the other hand, is not necessarily preserved by QED: if a left-handed spinor has its direction reversed by an electric field, its helicity flips. When particles are massless

QED interaction ψ ̄A/ψ = ψ ̄LA/ψL + ψ ̄RA/ψR is non-chiral, that is, it preserves chirality. Helicity, on the other hand, is not necessarily preserved by QED: if a left-handed spinor has its direction reversed by an electric field, its helicity flips. When particles are massless

In the massive case, it is also possible to take the non-relativistic limit. Then it is often better to talk about spin, the vector. Projecting on the direction of motion does not make so much sense when the particle is nearly at rest, or in a gas, say, when its direction of motion is constantly changing. The QED interactions do not preserve spin, however; only a strong magnetic field can flip an electron’s spin. So, as long as magnetic fields are weak, spin is a good quantum number. That is why spin is used in quantum mechanics.

QED, we hardly ever talk about chirality. The word is basically reserved for chiral theories, which are theories that are not symmetric under L ↔ R, such as the theory of the weak interactions. We talk very often about helicity. In the high-energy limit, helicity is often used interchangeably with chirality. As a slight abuse of terminology, we say ψL and ψR are helicity eigenstates. In the non-relativistic limit, we use helicity for photons and spin (the vector) for spinors. Helicity eigenstates for photons are circularly polarized light.

Quantum Field Theory and Standard Model by M. Schwartz

## Researcher

The motto in this section is: the higher the level of abstraction, the better.
Common Question 1
Common Question 2

Example1
Example2: