Is CPT-Invariance Sufficient for Lorentz Covariance and Locality?

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SUMMARY

The discussion centers on the relationship between CPT-invariance and its implications for locality and Lorentz covariance in quantum field theories. It is established that while the CPT theorem asserts that any local Lorentz-covariant quantum field theory is CPT-invariant, the converse does not hold true; there exist relativistic quantum theories that maintain CPT-invariance without being field theories. Furthermore, it is noted that CPT-invariance, when combined with specific restrictions on observables, leads to the conclusion that all observables can be expressed as functions of local Lorentz-invariant field operators.

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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.
 
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LastOneStanding said:
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.
 
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.
 

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