The problem of describing the quantum behavior of gravity, and thus understanding quantum spacetime, is still open. Loop quantum gravity is a well-developed approach to this problem. It is a mathematically well-defined background-independent quantization of general relativity, with its conventional matter couplings. Today research in loop quantum gravity forms a vast area, ranging from mathematical foundations to physical applications. Among the most significant results obtained so far are: (i) The computation of the spectra of geometrical quantities such as area and volume, which yield tentative quantitative predictions for Planck-scale physics. (ii) A physical picture of the microstructure of quantum spacetime, characterized by Planck-scale discreteness. Discreteness emerges as a standard quantum effect from the discrete spectra, and provides a mathematical realization of Wheeler's "spacetime foam" intuition. (iii) Control of spacetime singularities, such as those in the interior of black holes and the cosmological one. This, in particular, has opened up the possibility of a theoretical investigation into the very early universe and the spacetime regions beyond the Big Bang. (iv) A derivation of the Bekenstein-Hawking black-hole entropy. (v) Low-energy calculations, yielding n-point functions well defined in a background-independent context. The theory is at the roots of, or strictly related to, a number of formalisms that have been developed for describing background-independent quantum field theory, such as spin foams, group field theory, causal spin networks, and others. I give here a general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity, and a guide to the relevant literature.

中文翻译：

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循环量子引力。

描述引力的量子行为并由此理解量子时空的问题仍然悬而未决。圈量子引力是解决这个问题的一种成熟的方法。它是数学上明确定义的、与背景无关的广义相对论量化及其传统的物质耦合。如今，圈量子引力的研究形成了一个广阔的领域，从数学基础到物理应用。迄今为止获得的最重要的成果包括：（i）计算面积和体积等几何量的谱，这为普朗克尺度的物理学提供了初步的定量预测。(ii) 量子时空微观结构的物理图像，其特征是普朗克尺度的离散性。离散性作为离散光谱中的标准量子效应而出现，并提供了惠勒“时空泡沫”直觉的数学实现。(iii) 控制时空奇点，例如黑洞内部和宇宙学奇点。这尤其开启了对极早期宇宙和大爆炸之后的时空区域进行理论研究的可能性。(iv) 贝肯斯坦-霍金黑洞熵的推导。(v) 低能量计算，产生在与背景无关的上下文中明确定义的 n 点函数。该理论是许多为描述背景无关的量子场论而开发的形式主义的根源，或与之严格相关，例如自旋泡沫、群场论、因果自旋网络等。我在这里对这一候选量子引力理论的思想、技术、结果和悬而未决的问题进行了总体概述，并提供了相关文献的指南。