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

The first part of this paper extends the Doplicher-Haag-Roberts theory of s uperselection sectors to quantum field theory on arbitrary globally hyperbo lic spacetimes. The statistics of a superselection sector may be defined as in flat spacetime and each charge has a conjugate charge when the spacetim e possesses non-compact Cauchy surfaces. In this case, the held 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 appropria te 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 "modu lar covariance" for the Killing how yields a conformally covariant quantum field theory on the circle and a conformal spin-statistics theorem for char ged 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-stati stics theorem for charged covariant sectors where the spin is defined via t he SU(2)-covering of the spatial rotation group SO(3).