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Nuclearity, local quasiequivalence and split property for Dirac quantum fields in curved spacetime. (English) Zbl 1113.81104
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.

##### MSC:
 81T20 Quantum field theory on curved space or space-time backgrounds 81T05 Axiomatic quantum field theory; operator algebras 81R15 Operator algebra methods applied to problems in quantum theory 46N50 Applications of functional analysis in quantum physics
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