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Local definiteness, primarity and quasiequivalence of quasifree Hadamard quantum states in curved spacetime. (English) Zbl 0790.53077
Summary: 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 $$III_ 1$$-factors for sufficiently small regions in ultrastatic spacetimes.

##### MSC:
 53Z05 Applications of differential geometry to physics 83C47 Methods of quantum field theory in general relativity and gravitational theory
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