CPT Violation Does Not Lead to Violation of Lorentz Invariance and Vice Versa

TL;DR

This paper demonstrates that CPT violation does not necessarily imply Lorentz invariance violation and vice versa, especially in nonlocal quantum field theories with twisted Poincaré symmetry, challenging previous assumptions.

Contribution

It establishes a reciprocal relationship between CPT and Lorentz invariance, showing that violation of one does not imply violation of the other in certain nonlocal quantum field theories.

Findings

CPT violation can occur without Lorentz invariance violation.

Lorentz invariance violation does not necessarily lead to CPT violation under certain conditions.

Quantum corrections may cause particle-antiparticle property differences.

Abstract

We present a class of interacting nonlocal quantum field theories, in which the CPT invariance is violated while the Lorentz invariance is present. This result rules out a previous claim in the literature that the CPT violation implies the violation of Lorentz invariance. Furthermore, there exists the reciprocal of this theorem, namely that the violation of Lorentz invariance does not lead to the CPT violation, provided that the residual symmetry of Lorentz invariance admits the proper representation theory for the particles. The latter occurs in the case of quantum field theories on a noncommutative space-time, which in place of the broken Lorentz symmetry possesses the twisted Poincar\'e invariance. With such a CPT-violating interaction and the addition of a C-violating (e.g., electroweak) interaction, the quantum corrections due to the combined interactions could lead to different properties for the particle and antiparticle, including their masses.