We now cast the Dirac equation into a more apparent covariant form. Multiplying (5.3) by and defining
where , we have
In terms of the momentum operator we write
Introducing the Feynman dagger, or slash notation, for 4-vector , we have
Also notice that
We introduce the electromagnetic interaction by the usual minimal substitution
Let us study the properties of the matrices.
where the matrices are and . Although the Dirac matrices are written with Greek indices, they are not four vectors. Rather, they have the same value in every frame.
The matrices are anti-hermitian and is hermitian:
This can be summarized by writing
Using our previous representation (equation 5.10),