中文摘要：

介绍了在圈量子引力框架下应用边界BF理论对孤立视界熵做出统计解释的新方案.相比于以前的边界Chern-Simons理论方案,边界BF理论方案的最主要优点是,它适用于任意维度时空中的孤立视界.边界BF理论方案的可应用性非常广,包括任意维度时空中的Einstein理论、标量张量引力理论、以及引力与标量场非最小耦合理论.对于含有高阶导数项的Lovelock理论,在做了一定的假设以后,同样可以得到视界的熵.新方案既可解释Bekenstein-Hawking面积熵,也可解释Wald熵.文中提供了两种相关但又不同的具体实现方法.

英文摘要：

New approaches of the statistical explanation for the entropy of isolated horizons with the help of boundary BF theory in the framework of loop quantum gravity are reviewed. Seeing that the Palatini action of general relativity may reduce to the action of SO（1,1） BF theory at isolated horizons,two different but closely related approaches to statistically explain the entropy of isolated horizons by using the SO（1,1） BF theory are proposed. One is to start from the pure Palatini action. The variation shows that the symlectic structure of the theory consists of ordinary bulk term and a boundary term. The boundary term has the form of sympletic structure of an SO（1,1） BF theory. The boundary BF theory can be quantized in a similar way of boundary CS theory,and the bulk theory is quantized by loop quantization. Then,the entropy of isolated horizon may be explained by the dimension of Hilbert space of boundary BF theory. The other is to begin with the sum of Palatini action and the action of an SO（1,1） BF theory. After variation and identifying the SO（1,1） connection in boundary BF theory with the limit of non-rotating part of SO（3,1） connection on an isolated horizon,the symplectic structure is again obtained. Now,it only contains the bulk term. The boundary BF theory may split into free and interacting parts. We may quantize both the free part of BF theory and the bulk theory in loop quantization. The loop quantization of free part of BF theory provides a set of triangulation on the section of the isolated horizon. The interacting part provides a boundary condition for the bulk states. The entropy of isolated horizon is explained by the degree freedom of bulk quantum states which satisfy the boundary condition. Compared with the previous approach by using the boundary Chern-Simons theory,the most important advantage of the new approaches is that they are applicable to any isolated horizons in a spacetime with any dimension. It has been shown that the boundary BF theory approaches have wide app