From the reasoning so far it should be clear that there are different representations, in which spinors and the Dirac algebra can be written. These different representations are of great use when properties of the Dirac equation and of corresponding Lagrangians are to be investigated. For practical purposes, such as the claculation of cross sections, it should not matter in which representation the spinors are considered: As long as the correct degrees of freedom are properly taken into account, the cross section should be independent of the particular representation. This implies on the other hand that any representation can be chosen as long as the basic, representation-independent relations are fulfilled. These are the following:
- Anticommutator of the Dirac matrices:
- Definition of γ5:
- "Daggering" the γ matrices:
- E.o.M. for the Dirac spinors:
- Completeness relation, i.e. the normalization and energy projectors:
- Traces: From the anticommutator of two γ matrices and the symmetry prperties
of the trace (cyclicity of the arguments) the following identities follow:
