On the assertion that PCT violation implies Lorentz non-invariance

Out of conviction or expediency, some current research programs (Kostelecký (2008) [1], Kostelecký and Russell (2011) [2], Ferrero and Altschul (2011) [3], Anselmi (2009) [4]) take for granted that “PCT violation implies violation of Lorentz invariance”. We point out that this claim (Greenberg (2002) [5]) 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.