标题： 探索由量子物质产生的量子几何 显示英文标题

标题： Exploring quantum geometry created by quantum matter

摘要： 精确可解模型可以作为探索非微扰量子引力概念问题的优秀工具。 在微扰方法中，只有线性化引力场的两种辐射模式被量子化。 本研究的目标是探讨由物质源完全支配的量子几何的“库仑”方面。 由于三维空间中没有引力波，三维引力与物质的耦合为这一任务提供了理想的场所。 我们的分析将揭示量子引力的新方面，这些方面凸显了经典和半经典理论在未预见的领域中的局限性：广义相对论的非线性性可以将物质领域的微小量子涨落放大为引力领域的显著效应。 最后，这种分析导致了思想实验，这些实验清晰地表明了对物理现实本质的理解为何对所采用的理论视角极为敏感。 随着理论变得更加丰富，新的尺度出现，引发以前无法想象的新效应。 该模型为这一众所周知的链条提供了一个简洁的实现。 显示英文摘要

摘要： Exactly soluble models can serve as excellent tools to explore conceptual issues in non-perturbative quantum gravity. In perturbative approaches, it is only the two radiative modes of the linearized gravitational field that are quantized. The goal of this investigation is to probe the `Coulombic' aspects of quantum geometry that are governed entirely by matter sources. Since there are no gravitational waves in 3 dimensions, 3-d gravity coupled to matter provides an ideal arena for this task. Our analysis will reveal novel aspects of quantum gravity that bring out limitations of classical and semi-classical theories in unforeseen regimes: non-linearities of general relativity can magnify small quantum fluctuations in the matter sector to large effects in the gravitational sector. Finally, this analysis leads to thought experiments that bring out rather starkly why understanding of the nature of physical reality depends sensitively on the theoretical lens with which it is probed. As theories becomes richer, new scales emerge, triggering novel effects that could not be imagined before. The model provides a concise realization of this well-known chain.