LQG为困惑者
LQG for the Bewildered
摘要：
我们提出了一个教学介绍的概念基础上的连接制定的广义相对论-圈量子引力（LQG）-强调物理方面的框架。我们首先回顾广义相对论和量子场论，强调它们之间的相似之处，这些相似之处为建立量子引力理论奠定了基础。然后，我们以简洁明了的方式解释了从爱因斯坦-希尔伯特引力作用量到构造量子几何态（称为\emph{spin-networks}）的步骤，这些步骤为量子广义相对论的运动学希尔伯特空间提供了基础。一路上，我们介绍了各种相关的概念\emph{tetrads}，\emph{spin-connection}和\emph{holonomies}，这是一个先决条件，为理解LQG形式主义。在对LQG框架作了最小限度的介绍之后，我们讨论了它在黑洞熵和量子宇宙学问题上的应用。列出了对LQG最常见的批评，然后逐一解决，以使读者相信该理论的物理可行性。一套广泛的附录提供了几个关键概念的可访问的介绍，如\emph{Peter-Weyl theorem}，\emph{duality}的微分形式和\emph{Regge calculus}，等等。该演示文稿是针对研究生和研究人员谁有一定的量子力学和场论和/或广义相对论的工具熟悉，但通过现有的LQG文献浏览所需的看似技术实力吓倒。我们的希望是让形式主义对未入门的人来说显得不那么令人困惑，并帮助降低进入该领域的门槛。
英文摘要：
We present a pedagogical introduction to the notions underlying the connection formulation of General Relativity - Loop Quantum Gravity (LQG) - with an emphasis on the physical aspects of the framework. We begin by reviewing General Relativity and Quantum Field Theory, to emphasise the similarities between them which establish a foundation upon which to build a theory of quantum gravity. We then explain, in a concise and clear manner, the steps leading from the Einstein-Hilbert action for gravity to the construction of the quantum states of geometry, known as \emph{spin-networks}, which provide the basis for the kinematical Hilbert space of quantum general relativity. Along the way we introduce the various associated concepts of \emph{tetrads}, \emph{spin-connection} and \emph{holonomies} which are a pre-requisite for understanding the LQG formalism. Having provided a minimal introduction to the LQG framework, we discuss its applications to the problems of black hole entropy and of quantum cosmology. A list of the most common criticisms of LQG is presented, which are then tackled one by one in order to convince the reader of the physical viability of the theory. An extensive set of appendices provide accessible introductions to several key notions such as the \emph{Peter-Weyl theorem}, \emph{duality} of differential forms and \emph{Regge calculus}, among others. The presentation is aimed at graduate students and researchers who have some familiarity with the tools of quantum mechanics and field theory and/or General Relativity, but are intimidated by the seeming technical prowess required to browse through the existing LQG literature. Our hope is to make the formalism appear a little less bewildering to the un-initiated and to help lower the barrier for entry into the field.
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