# How to describe the spin state of a massless particle?

1. Sep 18, 2014

### ccnu

For a massive particle, say, an electron, we can use a spin vector $\vec{S}$ to denote its spin state, and the corresponding covariant four vector $S^\mu$. And we have $P \cdot S = 0$ in the particle rest frame, so it holds in any frame for it is an Lorentz scalor.
But, what if the particle is massless, so that it has no rest frame, how do we describe its spin state? I think $\vec{S}$ has no definition in this case.

Regards!

2. Sep 18, 2014

### jambaugh

One resolves the spin state into LH and RH chirality for massless particles. This is exactly the business with the left handed vs right handed neutrinos (assuming they were massless) and weak parity violation.

[EDIT]
Pardon me, chirality is defined for massive and massless cases, it is only that in the massless case chirality = helicity.
[END EDIT]

Last edited: Sep 18, 2014
3. Sep 18, 2014

### ccnu

Is that to say, we can only use chirality to describe the spin state? No spin vector be involved?