# An Algebraic Spin and Statistics Theorem

June 23, 1994

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.

open access link
Commun.Math.Phys.172:517-534,1995

@article{Guido:1995fy,
author = "Guido, Daniele and Longo, Roberto",
title = "{An Algebraic spin and statistics theorem}",
journal = "Commun. Math. Phys.",
volume = "172",
year = "1995",
pages = "517",
doi = "10.1007/BF02101806",
eprint = "funct-an/9406005",
archivePrefix = "arXiv",
primaryClass = "funct-an",
SLACcitation = "%%CITATION = FUNCT-AN/9406005;%%"
}

Keywords:

Spin and statistics, PCT, Superselection Theory, Bisognano-Wichmann