标题： 几何统计和映射类群的UIR 显示英文标题

标题： Geon Statistics and UIR's of the Mapping Class Group

摘要： 量子引力允许微观尺度的拓扑激发，这些激发可以表现为粒子——拓扑声子。 非平凡的空间拓扑也给理论带来了类似于QCD的$\theta$角的自由参数。 我们表明这些参数可以基于声子特性进行解释。 我们还发现，对于某些参数值，声子表现出新的粒子身份模式以及新的统计类型。 在这种情况下，声子的不可区分性由排列群的一个适当子群来表达，声子统计则由该子群的一个（可能为射影的）表示来表达。 显示英文摘要

摘要： Quantum Gravity admits topological excitations of microscopic scale which can manifest themselves as particles --- topological geons. Non-trivial spatial topology also brings into the theory free parameters analogous to the $\theta$-angle of QCD. We show that these parameters can be interpreted in terms of geon properties. We also find that, for certain values of the parameters, the geons exhibit new patterns of particle identity together with new types of statistics. Geon indistinguishability in such a case is expressed by a proper subgroup of the permutation group and geon statistics by a (possibly projective) representation of the subgroup.