A spin-statistics theorem for quantum fields on curved spacetime manifolds in a generally covariant framework

TL;DR

This paper develops a generally covariant quantum field theory framework on curved spacetimes, proving a spin-statistics theorem that links the correctness of spin-statistics connection to the non-triviality of quantum fields.

Contribution

It introduces a model-independent, locally covariant formulation of quantum fields on curved spacetimes and establishes a spin-statistics theorem within this framework.

Findings

If the spin-statistics connection is violated, all quantum fields become trivial.

The framework generalizes previous approaches to quantum field theory on curved spacetimes.

The theorem applies to quantum fields with fixed spinor or tensor types.

Abstract

A model-independent, locally generally covariant formulation of quantum field theory over four-dimensional, globally hyperbolic spacetimes will be given which generalizes similar, previous approaches. Here, a generally covariant quantum field theory is an assignment of quantum fields to globally hyperbolic spacetimes with spin-structure where each quantum field propagates on the spacetime to which it is assigned. Imposing very natural conditions such as local general covariance, existence of a causal dynamical law, fixed spinor- or tensor-type for all quantum fields of the theory, and that the quantum field on Minkowski spacetime satisfies the usual conditions, it will be shown that a spin-statistics theorem hols: If for some spacetimes the corresponding quantum field obeys the "wrong" connection between spin and statistics, then all quantum fields of the theory, on each spacetime, are trivial.