The notation $p_{a \dot{b}}$

Question

I am a mathematician and trying to learn scattering amplitude by reading Henriette Elvang and Yu-tin Huang's review Scattering Amplitudes (arXiv:1308.1697).

I have a question about the notation $p_{a \dot{b}}$ on page 10, (2.7). According to (2.7), $p_{a \dot{b}}$ is a two by two matrix which does not depend on $a, \dot{b}$. What is the meaning of $a, \dot{b}$? Why people use dot $\dot{b}$ (does it mean the derivative of $b$)?

My question is too elementary. Is it appropriate to ask this question here (if not, which website of Physics stack exchange should I use?).

Answer 1

This is a spinor index notation. There are 4 spinor spaces involved, the spinor bundle $S$, the dual spinor bundle $S^*$, the conjugate spinor bundle $\bar S$ and the dual conjugate spinor bundle $\bar S^*$. They each have the indices associated with them $\psi^a$, $\psi_a$, $\psi^{\dot a}$ and $\psi_{\dot a}$.