The spin-statistics theorem for TFTsConfirmed

by Luuk Stehouwer (Dalhousie University)

Thursday Sep 19, 2024, 11:00 a.m. → 12:30 p.m. America/Toronto

PI/4-400 - Space Room (Perimeter Institute for Theoretical Physics)

In quantum field theory (QFT) the spin-statistics theorem says that in a unitary QFT, a particle has half-integer spin if and only if it is a fermion. I show how to phrase this statement in the language of functorial field theories. More precisely, I explain when a functorial field theory "has fermions" and "has spinors" and when they are "related". I will then restrict to topological field theories (TFTs) and define unitary TFTs. There are counterexamples of the spin-statistics theorem for non-unitary TFTs. I will prove that every unitary TFT satisfies the spin-statistics theorem.