LOCAL DEFINITENESS, PRIMARITY AND QUASIEQUIVALENCE OF QUASI-FREE HADAMARD QUANTUM STATES IN CURVED SPACETIME

We prove that the GNS-representations of quasifree, Hadamard states on the Weyl-algebra of the quantized Klein-Gordon field propagating in an arbitrary globally hyperbolic spacetime are locally quasiequivalent. We also show that these representations satisfy local primarity and local definiteness if the spacetime is assumed to be ultrastatic. This implies that the local von Neumann algebras associated with these representations are type III1-factors for sufficiently small regions in ultrastatic spacetimes.