Symmetry of Spinor Components

Up to now in this chapter we have discussed the symmetry properties of spinors as a whole. The spinor itself is a four-component entity in which the rows correspond to spin orientations, the first and third to a spin, and the second and fourth to spin  

Partitioning the spinor into large and small components, we can write the 2-spinors in the form 

For a group such as C2 , which has a doubly degenerate fermion irrep, fhe group chain to C2 gives some information, but it does not resolve the division between Ai and A2, and B and 2- We therefore need a more general approach. 

We start by splitting each of the four spatial components of the spinor into a real and an imaginary part  

To elucidate the symmetry properties of the various parts here, we can start from the expressions for elimination of the small component, (4.82) and (4.83), 

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