# The spin-statistics theorem for TFTs

### APA

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

### MLA

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

### BibTex

@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}} }

**Collection**

**Subject**

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.