In QED, for example, charge conjugation commutes with the Lorentz group. It's an "internal" symmetry, not part of Lorentz (or Poincaré) symmetry.

However, a different kind of connection exists between charge conjugation and the Lorentz group, via the CPT theorem. The CPT theorem says that every relativistic QFT (satisfying certain axioms) has a symmetry that, among other things, reflects a timelike direction and an odd number of spatial directions. We call it the "CPT" theorem, but that's a little misleading, because it should be regarded as more fundamental (that is, more broadly applicable) than C, P, or T individually. In other words, we really ought to define charge conjugation in terms of CPT, not the other way around.

Here's the point: The general proof of the CPT theorem makes use of the *complex* Lorentz group (through the fact that correlation functions can be analytically continued to complex values of their spacetime arguments), and in this sense there is a kind of connection between C and Lorentz symmetry. This is reviewed in

and in the classic text by Streater and Wightman, *PCT, Spin and Statistics, and All That*.

This post imported from StackExchange Physics at 2020-11-26 15:40 (UTC), posted by SE-user Chiral Anomaly