弯曲时空中Dirac量子场的核性、局部拟等价性和分裂性
Nuclearity, Local Quasiequivalence and Split Property for Dirac Quantum Fields in Curved Spacetime
摘要：
我们证明了整体双曲时空上的自由Dirac量子场具有以下结构性质：（a）自由Dirac场代数上的任意两个准自由Hadamard态是局部准等价的，（b）任何准自由Hadamard态的表示都具有分裂性质;（c）如果基础时空是静态的，那么满足核性条件，即，与一个可扩展子系统（"盒子“）相关的自由能与盒子的体积有线性关系，并且对于大的温度$T$，自由能的变化类似于$\propto T^{s+1}$，其中$s+1$是时空的维数。
英文摘要：
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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