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

TL;DR

This paper extends superselection sector theory to quantum fields on curved spacetimes, establishing spin-statistics relations in black hole and symmetric spacetime contexts, with implications for quantum field theory in gravitational backgrounds.

Contribution

It generalizes the Doplicher-Haag-Roberts superselection sector framework to arbitrary curved spacetimes and derives new spin-statistics theorems under black hole and symmetry conditions.

Findings

Superselection sectors can be defined on curved spacetimes with non-compact Cauchy surfaces.

Spin-statistics theorems hold for sectors localized on Killing horizons and in symmetric black hole spacetimes.

Field nets and gauge groups can be constructed similarly to Minkowski spacetime in certain curved backgrounds.

Abstract

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).