Global Structure of Spacetime and Quantum Mechanics

(1)量子场论与裸奇性我们研究了1+1维量子场论的一个简单模型，以了解时间对裸奇性的影响。具体地说，我们通过将边界条件从Neumann突变到Dirichret来研究量子辐射。我们证明了辐射沿着从奇点开始发出的零测地线传播，这可以被称为雷霆。(2)黑洞和量子信息理论我们将量子信息理论应用到黑洞物理中。我们证明了黑洞视界外量子过程对广义熵的增加大于视界外代理准备的信息与无限远处观察者接收到的信息之间互信息的Holevo界。在最佳情况下，准备的信息可以完全检索。(3)信息论和宇宙学非齐次宇宙学模型的有效演化可能…更多可以用空间平均d个变量来描述。我们指出，在这种情况下，很自然地产生了一种与‘Kullback-Leibler相对信息熵’流体模型相同的度量，它表示了局部非均匀质量密度场与其在任意紧致区域上的空间平均值的可区分性。我们讨论了“有效信息”的时间演化，并探索了一些启示。我们推测，宇宙的信息量--通过包含尘埃物质的宇宙模型的相对信息熵来测量--正在增加。(4)黑洞的拓扑广义相对论数值研究的最新进展揭示了引力崩塌的有趣方面。黑洞的视界在拓扑上可以是一个环面，但它最终会变成一个球体。西诺用突变理论对所有可能的黑洞拓扑进行了分类。(5)非对易几何与量子宇宙西诺研究了因无理旋转不同的点的识别而引起的因子空间上的路径积分。他试图将这一点联系起来。具有非交换几何的空间。较少

(1) Quantum Field Theory and Naked SingularityWe have studied a simple model of quantum field theory in 1+1 dimensions to understand the effect of time like naked singularity. Specifically we have studied the quantum radiation by a sudden change of the boundary condition from Neumann to Dirichret. We showed that the radiation travels along the null geodesic emanating from the beginning of the singularity, which can be called "thunderbolt".(2) Black Hole and Quantum Information TheoryWe applied quantum information theory to black hole physics. We showed that the increase of the generalized entropy by quantum process outside the horizon of a black hole is more than the Holevo bound of mutual information between a message prepared by an agent located outside the horizon and that received by an observer at infinity. In the optimal case, the prepared information can be completely retrieved.(3) Information Theory and CosmologyThe effective evolution of an inhomogeneous cosmological model may … More be described in terms of spatially average d variables. We point out that in this context, quite naturally, a measure arises which is identical to a fluid model of the 'Kullback--Leibler Relative Information Entropy', expressing the distinguishability of the local inhomogeneous mass density field from its spatial average on arbitrary compact domains. We discuss the time-evolution of 'effective information' and explore some implications. We conjecture that the information content of the Universe - measured by Relative Information Entropy of a cosmological model containing dust matter -- is increasing.(4) Topology of Black HoleRecent development of numerical study of general relativity reveals interesting aspect in the gravitational collapse. The event horizon of a black hole can be topologically a torus but it becomes a sphere eventually. Siino has classified all the possible topologies of black holes using the catastrophe theories.(5) Non-commutative Geometry and Quantum UniverseSiino has studied a path integral over factor spaces induced by identification of points which differ by irrational rotations. He has attempted to link this. space with non-commutative geometries. Less