An Algebraic Spin and Statistics Theorem

TL;DR

This paper establishes a spin-statistics and PCT theorem within Quantum Field Theory by leveraging the geometric action of modular groups on local observable algebras, based on a natural assumption related to Lorentz transformations.

Contribution

It introduces a novel algebraic approach to derive fundamental theorems in QFT using modular theory and superselection sectors, under a natural geometric assumption.

Findings

Proves a spin-statistics theorem in 4D QFT

Derives a PCT theorem from modular group actions

Connects geometric modular actions with fundamental symmetries

Abstract

A spin-statistics theorem and a PCT theorem are obtained in the context of the superselection sectors in Quantum Field Theory on a 4-dimensional space-time. Our main assumption is the requirement that the modular groups of the von Neumann algebras of local observables associated with wedge regions act geometrically as pure Lorentz transformations. Such a property, satisfied by the local algebras generated by Wightman fields because of the Bisognano-Wichmann theorem, is regarded as a natural primitive assumption.