Spin-Statistics, Spin-Locality, and TCP: Three Distinct Theorems

TL;DR

This paper clarifies the differences among three fundamental theorems in quantum field theory—spin-statistics, spin-locality, and TCP—highlighting their distinct assumptions, dependencies, and implications for fields like quarks and gluons.

Contribution

The paper distinguishes the spin-statistics theorem from the spin-locality theorem, clarifies their assumptions, and discusses their applicability to fields without asymptotic limits.

Findings

The spin-statistics theorem depends on properties of asymptotic free fields.

Ghost fields can evade both the spin-statistics and spin-locality theorems.

The TCP theorem has weaker assumptions compared to the other theorems.

Abstract

I show that the spin-statistics theorem has been confused with another theorem that I call the spin-locality theorem. I also argue that the spin-statistics theorem properly depends on the properties of asymptotic fields which are free fields. In addition, I discuss how ghosts evade both theorems, give the basis of the spin-statistics theorem for fields without asymptotic limits such as quark and gluon fields, and emphasise the weakness of the requirements for the $TCP$ theorem.