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

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

2001-06-27

arxiv.org/abs/math-ph/0106028v3

Commun.Math.Phys. 261 (2006) 133-159

Physics

Mathematical Physics

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

Scientific paper

10.1007/s00220-005-1398-2

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.

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