Using the anticommutators of the gamma matrices, one can show that for any and ,
where is the identity matrix in four dimensions.
Further identities can be read off directly from the gamma matrix identities by replacing the metric tensor with inner products. For example,
where is the Levi-Civita symbol.
Often, when using the Dirac equation and solving for cross sections, one finds the slash notation used on four-momentum: using the Dirac basis for the gamma matrices,
as well as the definition of four-momentum,
we see explicitly that
Similar results hold in other bases, such as the Weyl basis.