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CPT violation implies violation of Lorentz invariance.

O. W. Greenberg

2002 · DOI: 10.1103/PhysRevLett.89.231602
Physical Review Letters · 375 Citations

TLDR

A interacting theory that violates CPT invariance necessarily violates Lorentz invariance, and theories that violate CPT by having different particle and antiparticle masses must be nonlocal.

Abstract

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.