# Why are twistors commuting?

In his book, Srednicki introduces the notion of twistor in chapter 50. It is described as a simply commuting spinor, as opposed to anti-commuting. How do we know that this object is simply commuting? Since it carries a spinor index, I expected the opposite.

Presumably OP is worried that the spin-statistics theorem states that spin $$1/2$$ fields should be described by Grassmann-odd (as opposed to Grassmann-even) fields. Recall that in the Dirac field, the Grassmann-odd nature sits in the creation and annihilation operators.
On the other hand, the Dirac spinors $$u_s({\bf p})$$ and $$v_s({\bf p})$$, which Ref. 1 discusses, are Grassmann-even. In particular the commuting spinor $$\phi_a$$ that Ref. 1 mentions around eq. (50.8) is a Grassmann-even left-handed Weyl spinor.