Elimination for Different Representations of Dirac Matrices

As a side remark, we may note that elimination procedures such as the one just discussed depend on the choice of the Dirac matrices see section 5.2. All that has been said so far holds for the standard representation, for which we have in split notation. 

If we now seek to eliminate the small component, we must always solve that equation which does not contain the derivative of In the case of the standard representation we therefore rearrange the second one, Eq. (13.89), 

we do not gain anything from the Weyl representation when subjected to an elimination procedure. 

---