标题： 环量子引力中的自同构 显示英文标题

标题： Automorphisms in Loop Quantum Gravity

摘要： 我们研究环量子引力中空间微分同胚群的某种分布扩展。 这种扩展由路径群oid P的自同构Aut(P)给出，是由Velhinho提出的，并受到范畴论的启发。 这个群比分段解析微分同胚群要大得多。 特别是，我们将证明具有相同组合结构但不同广义纽结类的图可以相互映射。 我们描述了自同构不变的希尔伯特空间，并评论了如何可能出现LQG的组合表述。 显示英文摘要

摘要： We investigate a certain distributional extension of the group of spatial diffeomorphisms in Loop Quantum Gravity. This extension, which is given by the automorphisms Aut(P) of the path groupoid P, was proposed by Velhinho and is inspired by category theory. This group is much larger than the group of piecewise analytic diffeomorphisms. In particular, we will show that graphs with the same combinatorics but different generalized knotting classes can be mapped into each other. We describe the automorphism-invariant Hilbert space and comment on how a combinatorial formulation of LQG might arise.