PIRSA:24090177

The spin-statistics theorem for TFTs

(2024). The spin-statistics theorem for TFTs. Perimeter Institute. https://pirsa.org/24090177

The spin-statistics theorem for TFTs. Perimeter Institute, Sep. 19, 2024, https://pirsa.org/24090177 

          @misc{ pirsa_PIRSA:24090177,
            doi = {10.48660/24090177},
            url = {https://pirsa.org/24090177},
            author = {},
            keywords = {Mathematical physics},
            language = {en},
            title = {The spin-statistics theorem for TFTs},
            publisher = {Perimeter Institute},
            year = {2024},
            month = {sep},
            note = {PIRSA:24090177 see, \url{https://pirsa.org}}
          }
Luuk Stehouwer
Talk number
PIRSA:24090177
Collection
Talk Type
Subject
Abstract

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.