Dirac Equation: Gamma Matrices as 4-Vector Components?

[vijaychitgopka]

While studying the Dirac Equation, we come across the gamma matrices. Can we consider these matrices as the components
of a 4-vector ?

 

[CharlesFrancis]

This is the defining condition for the Dirac matrices. It is not derived, because it is a definition. It is required to allow the factorisation of the Klein Gordon equation in the derivation of the Dirac equation.

 

[Bill_K]

While studying the Dirac Equation, we come across the gamma matrices. Can we consider these matrices as the components of a 4-vector ?

No, the Dirac matrices are the Clebsch-Gordan coefficients that couple the product of two Dirac spinors to form a 4-vector. The result ψγ^μψ is a 4-vector.