Nuclearity, local quasiequivalence and split property for Dirac quantum fields in curved spacetime
The authors present several structural properties for a free Dirac quantum field on a globally hyperbolic spacetime. They prove that any two quasifree Hadamard states on the algebra of free Dirac fields are locally quasiequivalent and, on a globally hyperbolic spacetime, the associated local von Neumann algebras are factors of type III\(_1\) which are locally unitarily equivalent. They verify that the theory of a free Dirac field on a static spacetime satisfies the nuclearity condition in the sense of Buchholz and Wichmann. Using this result they prove that on a globally hyperbolic spacetime, the split-property holds in the representation of any quasifree Hadamard state.
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