Pragmatists and purists on CPT invariance in relativistic quantum field theories

An influential claim in the physics literature states that the violation of CPT invariance in an interacting RQFT entails the violation of Lorentz invariance. This claim is surprising since standard proofs of the CPT theorem require more assumptions than Lorentz invariance, and are restricted to non-interacting, or at best, unrealistic interacting theories. This essay analyzes this claim in the context of the debate between pragmatist approaches to RQFTs, which trade mathematical rigor for the ability to derive predictions from realistic interacting theories, and purist approaches, which trade the ability to formulate realistic interacting theories for mathematical rigor.