On the spin-statistics connection in curved spacetimes

TL;DR

This paper generalizes the spin-statistics connection within locally covariant quantum field theory, providing a more operational framework and extending the relation to curved spacetimes using a functorial approach.

Contribution

It introduces a functorial formulation of locally covariant theories, enabling a broader derivation of the spin-statistics connection in curved spacetimes.

Findings

Generalized spin-statistics relation for curved spacetimes

Operational description of theories with spin

Rigidity argument transferring properties from Minkowski to curved spacetimes

Abstract

The connection between spin and statistics is examined in the context of locally covariant quantum field theory. A generalization is proposed in which locally covariant theories are defined as functors from a category of framed spacetimes to a category of $*$-algebras. This allows for a more operational description of theories with spin, and for the derivation of a more general version of the spin-statistics connection in curved spacetimes than previously available. The proof involves a "rigidity argument" that is also applied in the standard setting of locally covariant quantum field theory to show how properties such as Einstein causality can be transferred from Minkowski spacetime to general curved spacetimes.