标题： 自旋网络与环量子引力中的再耦合 显示英文标题

标题： Spin Networks and Recoupling in Loop Quantum Gravity

摘要： 我讨论自旋网络基和再耦合理论（在其图形辫子理论表述中的作用）及其在环量子引力中进行显式计算的使用。 特别是，我表明再耦合理论允许推导出量子体积算符本征值的显式表达式。 这些计算的一个重要附带结果是确定了一个标量积，在该标量积下面积和体积算符是对称的，自旋网络态是正交归一的。 显示英文摘要

摘要： I discuss the role played by the spin-network basis and recoupling theory (in its graphical tangle-theoretic formulation) and their use for performing explicit calculations in loop quantum gravity. In particular, I show that recoupling theory allows the derivation of explicit expressions for the eingenvalues of the quantum volume operator. An important side result of these computations is the determination of a scalar product with respect to which area and volume operators are symmetric, and the spin network states are orthonormal.