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Converse of the CPT theorem

  1. Apr 17, 2013 #1
    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.
  2. jcsd
  3. Apr 17, 2013 #2


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    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.
  4. Apr 17, 2013 #3
    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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