标题： 黑洞状态计数在环量子引力中 显示英文标题

标题： Black hole state counting in loop quantum gravity

摘要： 在环量子引力的U(1)表述中讨论了计算黑洞微观状态的两种方法，一种是计算所有允许的自旋网络标签j,m，另一种仅计算m标签。明确了m的约束条件，并讨论了通量量子数与m之间的映射。展示了当涉及大区域时，|m|=j的配置有时被寻求，但只有在大区域情况下才重要。讨论扩展到了SU(2)表述。 显示英文摘要

摘要： The two ways of counting microscopic states of black holes in the U(1) formulation of loop quantum gravity, one counting all allowed spin network labels j,m and the other only m labels, are discussed in some detail. The constraints on m are clarified and the map between the flux quantum numbers and m discussed. Configurations with |m|=j, which are sometimes sought after, are shown to be important only when large areas are involved. The discussion is extended to the SU(2) formulation.