论文标题
在全球双曲机上的PROCA字段的量化：Hadamard States和Møller操作员
The quantization of Proca fields on globally hyperbolic spacetimes: Hadamard states and Møller operators
论文作者
论文摘要
本文讨论了关于全球双曲线时空中实际Proca领域代数量化的几个问题，以及该领域的Hadamard国家的定义和存在。特别是，延长了以前的工作，我们构建了所谓的Møller$*$ - 在帕拉卡司法相关的空间上可观察到的proca可观察物的代数之间的同构，证明这些同构的回调保留在两个空间上定义的相应quasifree态的hadamard属性。然后，我们沿着$*$ - 同构的超级几何形状的超级空间上构建了一个天然的hadamard状态，以在全球一般具有全球双曲线时空上获得Hadamard状态。我们通过比较了Hadamard状态的定义，在此处以Wavefront集进行了比较，该论文与Lee-Sters和Pfenning提出的一篇有关，该论文利用了补充的Klein-Gordon Hadamard形式。我们建立了两个定义的（几乎）完全等效。
This paper deals with several issues concerning the algebraic quantization of the real Proca field in a globally hyperbolic spacetime and the definition and existence of Hadamard states for that field. In particular, extending previous work, we construct the so-called Møller $*$-isomorphism between the algebras of Proca observables on paracausally related spacetimes, proving that the pullback of these isomorphisms preserves the Hadamard property of corresponding quasifree states defined on the two spacetimes. Then, we pull-back a natural Hadamard state constructed on ultrastatic spacetimes of bounded geometry, along this $*$-isomorphism, to obtain a Hadamard state on a general globally hyperbolic spacetime. We conclude the paper, by comparing the definition of a Hadamard state, here given in terms of wavefront set, with the one proposed by Fewster and Pfenning, which makes use of a supplementary Klein-Gordon Hadamard form. We establish an (almost) complete equivalence of the two definitions.
