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

TL;DR

This paper investigates the structural properties of free Dirac quantum fields in curved spacetime, demonstrating local quasiequivalence of states, the split property, and nuclearity conditions in static spacetimes, with implications for quantum field theory in curved backgrounds.

Contribution

It establishes the local quasiequivalence, split property, and nuclearity conditions for Dirac fields in curved spacetime, extending the understanding of quantum field structures in such settings.

Findings

Any two quasifree Hadamard states are locally quasiequivalent.

The split property holds in the representation of any quasifree Hadamard state.

Nuclearity condition is satisfied in static spacetimes, with free energy scaling linearly with volume and temperature.

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.