标题： 新的2+1重力环表示 显示英文标题

标题： New Loop Representations for 2+1 Gravity

摘要： 由于2+1维广义相对论背后的规范群是非紧致的，在从联络过渡到环路表示的过程中会出现一些困难。 本文证明了通过适当地选择出现在环路变换定义中的测度，这些问题是可以处理的。因此，“老式”的基于普通闭合曲线的环路表示确实存在。 当空间拓扑为二维环面时，这些表示可以明确构造出来；{\it 所有}量子态可以表示为（同伦类的）环路函数，且标量积和基本可观测量的作用可以直接用环路来表达。 显示英文摘要

摘要： Since the gauge group underlying 2+1-dimensional general relativity is non-compact, certain difficulties arise in the passage from the connection to the loop representations. It is shown that these problems can be handled by appropriately choosing the measure that features in the definition of the loop transform. Thus, ``old-fashioned'' loop representations - based on ordinary loops - do exist. In the case when the spatial topology is that of a two-torus, these can be constructed explicitly; {\it all} quantum states can be represented as functions of (homotopy classes of) loops and the scalar product and the action of the basic observables can be given directly in terms of loops.