Anomalies in terminology: symmetries in physics
I’m working on some research with my friend Barry involving CPT reference frame resources and simultaneously am teaching Elementary Particle Physics which has led to an annoying discovery: we (meaning all physicists) play fast and loose too often with our terminology. The annoying examples I have found have to do with CPT and related symmetries. Specifically, it seems we have a tendency to mix our definitions a bit.
So, for example, Barry co-wrote a paper on time-reversal resources a few years ago in which (what I would call) the “standard” interpretation of time-reversal is used: the time-reversal operator swaps the sign of both the momentum and time coordinates of a particle while leaving the rest of its properties unchanged. Conversely, the action of parity is to swap the chirality (handedness) of a particle by simultaneously changing the sign of all its spatial components. However, in the book Quantum Field Theory for Mathematicians, Robin Ticciati says that the effect of “…parity on fermion particle states reverses momentum…” while leaving other properties unchanged. Now it’s not that either one is necessarily wrong (since Ticciati’s definition is self-consistent with the rest of the book) it’s that the terminology is getting a bit muddled.
As another example, the book from which I am teaching the particle physics class, Introduction to Elementary Particles by David Griffiths makes a common simplification that also happens to be misleading: it essentially mixes the notions of chirality and helicity. These two concepts are only equivalent for massless particles! The importance of this distinction becomes apparent when working with charge conjugation. In a nutshell, the charge conjugation operator turns a particle into its own anti-particle meaning that it changes the sign of all of a particle’s internal quantum numbers. But it turns out to be basis-dependent and, in some bases, it also swaps the chirality! In other words, it can be defined to include parity. In fact, it appears as if it has to be if Majorana spinors are to act as a self-conjugate basis.
In short, we need to be consistent! In this case, we need consistent terminology and definitions for parity, chirality, helicity, and time-reversal. And I need to figure out how to write this up so as not to confuse any readers.