ABSTRACT
This chapter discusses the covariances of the KG and Dirac equations, concentrating mainly on the latter. It considers Lorentz transformations and discusses the scalar KG wavefunction and the 4-component Dirac spinor must transform in order that the respective equations be covariant under these transformations. The case of the Dirac equation is more complicated, because the wavefunction has more than one component, corresponding to the fact that it describes a spin-1/2 particle. Very much the same thing happens in the case of spinor wavefunctions, except that they transform in a way different from – though closely related to – that of vectors. In the present section we shall discuss how this works for three-dimensional rotations of the spatial coordinate system, and explain how it generalizes to boosts, which include transformations of the time coordinate as well.
