PIRSA:24090177 Scientific Series Mathematical physics

DOI10.48660/24090177

Series: Mathematical Physics

(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}}
}

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.

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