# Charged sectors, spin and statistics in quantum field theory on curved spacetimes

June 22, 1999

The first part of this paper extends the Doplicher-Haag-Roberts theory of superselection sectors to quantum field theory on arbitrary globally hyperbolic spacetimes. The statistics of a superselection sector may be defined as in flat spacetime and each charge has a conjugate charge when the spacetime possesses non-compact Cauchy surfaces. In this case, the field net and the gauge group
can be constructed as in Minkowski spacetime.
The second part of this paper derives spin-statistics theorems on spacetimes with appropriate symmetries. Two situations are considered: First, if the spacetime has a bifurcate Killing horizon, as is the case in the presence of black holes, then restricting the observables to the Killing horizon together with "modular covariance" for the Killing flow yields a conformally covariant quantum field theory on the circle and a conformal spin-statistics theorem for charged sectors localizable on the Killing horizon. Secondly, if the spacetime has a rotation and PT symmetry like the Schwarzschild-Kruskal black holes, "geometric modular action" of the rotational symmetry leads to a spin-statistics theorem for charged covariant sectors where the spin is defined via the SU(2)-covering of the spatial rotation group SO(3).

open access link
Rev.Math.Phys. 13 (2001) 125-198

@article{Guido:1999xu,
author = "Guido, D. and Longo, R. and Roberts, J. E. and Verch, R.",
title = "{Charged sectors, spin and statistics in quantum field
theory on curved space-times}",
journal = "Rev. Math. Phys.",
volume = "13",
year = "2001",
pages = "125-198",
doi = "10.1142/S0129055X01000557",
eprint = "math-ph/9906019",
archivePrefix = "arXiv",
primaryClass = "math-ph",
SLACcitation = "%%CITATION = MATH-PH/9906019;%%"
}

Keywords:

Superselection Theory, QFT on curved spacetimes