The measurement process is considered for quantum field theory on curved spacetimes. Measurements are carried out on one QFT, the "system", using another, the "probe" via a dynamical coupling of "system" and "probe" in a bounded spacetime region. The resulting "coupled theory" determines a scattering map on the uncoupled combination of the "system" and "probe" by reference to natural "in" and "out" spacetime regions. No specific interaction is assumed and all constructions are local and covariant. Given any initial probe state in the "in" region, the scattering map determines a completely positive map from "probe" observables in the "out" region to "induced system observables", thus providing a measurement scheme for the latter. It is shown that the induced system observables may be localized in the causal hull of the interaction coupling region and are typically less sharp than the probe observable, but more sharp than the actual measurement on the coupled theory. Post-selected states conditioned on measurement outcomes are obtained using Davies-Lewis instruments. Composite measurements involving causally ordered coupling regions are also considered. Provided that the scattering map obeys a causal factorization property, the causally ordered composition of the individual instruments coincides with the composite instrument; in particular, the instruments may be combined in either order if the coupling regions are causally disjoint. This is the central consistency property of the proposed framework. The general concepts and results are illustrated by an example in which both "system" and "probe" are quantized linear scalar fields, coupled by a quadratic interaction term with compact spacetime support. System observables induced by simple probe observables are calculated exactly, for sufficiently weak coupling, and compared with first order perturbation theory.

中文翻译：

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量子场和局部测量

测量过程被考虑用于弯曲时空的量子场论。测量是在一个 QFT（“系统”）上进行的，使用另一个 QFT（“探针”）通过“系统”和“探针”在有界时空区域中的动态耦合进行。由此产生的“耦合理论”通过参考自然“输入”和“输出”时空区域来确定“系统”和“探测器”的非耦合组合上的散射图。没有假设特定的相互作用，所有结构都是局部的和协变的。给定“in”区域中的任何初始探测状态，散射图确定从“out”区域中的“probe”可观测值到“诱导系统可观测值”的完全正映射，从而为后者提供测量方案。结果表明，诱导系统可观测量可能位于相互作用耦合区域的因果包中，通常不如探针可观测量清晰，但比耦合理论的实际测量更清晰。使用 Davies-Lewis 仪器获得以测量结果为条件的后选择状态。还考虑了涉及因果有序耦合区域的复合测量。如果散射图服从因果分解属性，则单个仪器的因果有序组成与复合仪器一致；特别是，如果耦合区域在因果关系上不相交，则可以按任一顺序组合仪器。这是所提议框架的核心一致性属性。一般概念和结果通过一个例子来说明，其中“系统”和“探针”都是量化的线性标量场，通过具有紧凑时空支持的二次交互项耦合。对于足够弱的耦合，由简单探针观测值引起的系统观测值被精确计算，并与一阶微扰理论进行比较。