标题： 关于量子引力（QGR）的弯曲时空极限上的量子场论（QFT）。 第一部分：一般方案 显示英文标题

标题： Towards the QFT on Curved Spacetime Limit of QGR. I: A General Scheme

摘要： 本文以及其姊妹篇致力于探讨如何从量子广义相对论（QGR）出发，基于第一性原理，得到经典时空（CST）上普通物质量子场（QFT）的半经典极限。我们强调，并非声称已经圆满解答了这一问题，而是希望通过展示完成该计划所面临的难题，激发讨论。 在本文中，我们提出了一种可能遵循的方案以达到这种极限。我们讨论了执行此方案时出现的技术和概念问题，以及它们原则上可以如何解决。正如预期的那样，由于QGR是一种背景独立理论，因此会出现完全新的问题。例如，从根本上讲，光子的概念不仅涉及麦克斯韦量子场，还涉及度规算符——可以说不存在“光子真空态”，而存在“光子真空算符”！ 虽然在这第一篇文章中我们侧重于概念性和抽象方面，比如定义（基本的）n粒子态（例如光子），但在第二篇文章中我们将进行详细的计算，其中包括相干态期望值以及随机格点上的传播。这些计算展示了目前的数学技术能够达到的程度。尽管这些计算得出了关于量子修正（例如伽马射线暴效应）大小的具体预测，但这些预测不应过于认真对待，因为a) 计算仅在运动学层面进行，b) 虽然我们可以分类我们的构造中的自由度量，但对可能选择的物理意义的分析才刚刚开始。 显示英文摘要

摘要： In this article and a companion paper we address the question of how one might obtain the semiclassical limit of ordinary matter quantum fields (QFT) propagating on curved spacetimes (CST) from full fledged Quantum General Relativity (QGR), starting from first principles. We stress that we do not claim to have a satisfactory answer to this question, rather our intention is to ignite a discussion by displaying the problems that have to be solved when carrying out such a program. In the present paper we propose a scheme that one might follow in order to arrive at such a limit. We discuss the technical and conceptual problems that arise in doing so and how they can be solved in principle. As to be expected, completely new issues arise due to the fact that QGR is a background independent theory. For instance, fundamentally the notion of a photon involves not only the Maxwell quantum field but also the metric operator - in a sense, there is no photon vacuum state but a "photon vacuum operator"! While in this first paper we focus on conceptual and abstract aspects, for instance the definition of (fundamental) n-particle states (e.g. photons), in the second paper we perform detailed calculations including, among other things, coherent state expectation values and propagation on random lattices. These calculations serve as an illustration of how far one can get with present mathematical techniques. Although they result in detailed predictions for the size of first quantum corrections such as the gamma-ray burst effect, these predictions should not be taken too seriously because a) the calculations are carried out at the kinematical level only and b) while we can classify the amount of freedom in our constructions, the analysis of the physical significance of possible choices has just begun.