CPT violation implies violation of Lorentz invariance.
@article{Greenberg2002CPTVI, title={CPT violation implies violation of Lorentz invariance.}, author={O. W. Greenberg}, journal={Physical review letters}, year={2002}, volume={89 23}, pages={ 231602 } }
A interacting theory that violates CPT invariance necessarily violates Lorentz invariance. On the other hand, CPT invariance is not sufficient for out-of-cone Lorentz invariance. Theories that violate CPT by having different particle and antiparticle masses must be nonlocal.
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