Nuclearity, local quasiequivalence and split property for Dirac quantum fields in curved spacetime

We show that a free Dirac quantum field on a globally hyperbolic spacetime has the following structural properties: (a) any two quasifree Hadamard states on the algebra of free Dirac fields are locally quasiequivalent; (b) the split-property holds in the representation of any quasifree Hadamard state; (c) if the underlying spacetime is static, then the nuclearity condition is satisfied, that is, the free energy associated with a finitely extended subsystem ("box") has a linear dependence on the volume of the box and goes like proportional to Ts+1 for large temperatures T, where s+1 is the number of dimensions of the spacetime.