Nuclearity, Local Quasiequivalence and Split Property for Dirac Quantum Fields in Curved Spacetime

Abstract

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 $\propto T^{s+1}$ for large temperatures $T$, where $s+1$ is the number of dimensions of the spacetime.

Latex, 33 pages, no figures. v3: Corrections to the proofs of thm. 4.1 and thm. 3.1 and more references