On the assertion that PCT violation implies Lorentz non-invariance

TL;DR

This paper challenges the assumption that PCT violation necessarily implies Lorentz invariance violation, demonstrating through causal perturbation theory that PCT symmetry can be preserved during renormalization.

Contribution

It provides a theoretical proof that local PCT-invariant interactions can retain PCT symmetry after renormalization, questioning previous assumptions.

Findings

PCT violation does not automatically imply Lorentz invariance violation

PCT symmetry can be maintained during renormalization with local interactions

The evidence linking PCT violation to Lorentz invariance violation remains inconclusive

Abstract

Out of conviction or expediency, some current research programs take for granted that "PCT violation implies violation of Lorentz invariance". We point out that this claim is still on somewhat shaky ground. In fact, for many years there has been no strengthening of the evidence in this direction. However, using causal perturbation theory, we prove here that when starting with a local PCT-invariant interaction, PCT symmetry can be maintained in the process of renormalization.