G. L\"uders and W. Pauli proved the $\mathcal{ CPT}$ theorem based on Lagrangian quantum field theory almost half a century ago. R. Jost gave a more general proof based on ``axiomatic'' field theory nearly as long ago. The axiomatic point of view has two advantages over the Lagrangian one. First, the axiomatic point of view makes clear why $\mathcal{ CPT}$ is fundamental--because it is intimately related to Lorentz invariance. Secondly, the axiomatic proof gives a simple way to calculate the $\mathcal{ CPT}$ transform of any relativistic field without calculating $\mathcal{ C}$, $\mathcal{ P}$ and $\mathcal{ T}$ separately and then multiplying them. The purpose of this pedagogical paper is to ``deaxiomatize'' the $\mathcal{ CPT}$ theorem by explaining it in a few simple steps. We use theorems of distribution theory and of several complex variables without proof to make the exposition elementary.
Categories: hep-ph hep-th nucl-th