Canonical commutation rules for Minkowski spacetime
induce the following commutation relations on the twistor space:
One way of quantising the theory is to use the following substitution:
The spin operator can be easily derived in the non-commutative case following the same procedure. The result is the symmetrised form:
Therefore, if we want a twistor function 
to be an eigenstate of spin operator with eigenvalue 
, f must be homogeneous of degree -2s-2.