Textbooks often define chirality on the level of the fields but not on the level of the states. How does one define chirality on the level of one-particle states?
It is clear how one can define chirality on the level of fields $\psi^{\alpha}(x)$, as Lorentz indices such as $\alpha$ (which may be a vector index $\mu$ for a spin-1 massive field or a spinor index $\alpha$ for a spin-1/2 massive field) as these indices transform directly under the Lorentz group, and representations of the Lorentz group have a definite notion of handedness i.e. finite reps are classified by two half integers $(A,B)$ and the $(1/2,0)$ rep is said to be left handed and $(0,1/2)$ to be right handed. However it is unclear how there is a notion of handedness on the level of massive states $|p^{\mu},\sigma\rangle$. It is unclear because the states transform under representations of the little group, which for massive particles is $SO(3)$, and representations of $SO(3)$ by themselves do not have a notion of handedness.
Q: what is the definition of chirality purely on the level of the states?
