Why is CPT fundamental?

Abstract

G. Lüders and W. Pauli proved the $\mathcal{C}\mathcal{P}\mathcal{T}$ 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 $\mathcal{C}\mathcal{P}\mathcal{T}$ is fundamental--because it is intimately related to Lorentz invariance. Secondly, the axiomatic proof gives a simple way to calculate the $\mathcal{C}\mathcal{P}\mathcal{T}$ 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 $\mathcal{C}\mathcal{P}\mathcal{T}$ 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.

17 pages, no figures

References in corpus (3)

• A model of CPT violation for neutrinos
• Failure of microcausality in quantum field theory on noncommutative spacetime
• Hybrid Dirac Fields

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