Is CPT-Invariance Sufficient for Lorentz Covariance and Locality?

[VantagePoint72]

In its standard formulation, the CPT theorem says that any local Lorentz-covariant quantum field theorem will be CPT-invariant. What of the theorem's converse? I would suspect CPT-invariance alone would be too weak to guarantee locality and Lorentz-covariance, but are there perhaps additional restrictions that, combined with CPT-invariance, will do so? I've tried looking through some of the literature, but I can't find any analysis of this.

 

[DarMM]

In its standard formulation, the CPT theorem says that any local Lorentz-covariant quantum field theorem will be CPT-invariant. What of the theorem's converse? I would suspect CPT-invariance alone would be too weak to guarantee locality and Lorentz-covariance, but are there perhaps additional restrictions that, combined with CPT-invariance, will do so? I've tried looking through some of the literature, but I can't find any analysis of this.

The converse is not true. There are relativistic quantum theories obeying CPT-invariance that are not field theories.

In relation to the second question, CPT-invariance and certain restrictions on the observables basically imply that all observables are functions of local Lorentz-invariant field operators.

 

[VantagePoint72]

Thank you. Do you know of a text or paper where I can read more on your second comment? I'd like to understand exactly what is necessary for implying Lorentz covariance.