标题： 热和两粒子应力-能量在2维Misner时空的纪元地平线上必须是未定义的 显示英文标题

标题： The thermal and two-particle stress-energy must be ill-defined on the 2-d Misner space chronology horizon

摘要： 我们证明，四维图像和方法的一个类似方法可以用来重现克拉斯尼科夫的结果，即对于二维米斯纳空间初始全局双曲区域IGH上的实无质量标量场模型，存在两个粒子和热的哈达玛态（构建在共形真空中），使得这些态中重整化的应力-能量张量的期望值在IGH上为零。 然而，我们将证明凯、拉德齐科夫斯基和沃尔德的一般定理结论仍然适用于这些态。 也就是说，在这些态中的任何一个态中，对于柯西视界上的任何一点b以及b的任何邻域N，至少存在一对非类空相关的点(x,x')，其中x和x'属于IGH与N的交集，使得其两点函数的某种微分形式是奇异的。 （我们通过证明这些态的两点函数与它们所构建的共形真空具有相同的奇异性来证明这一点。） 换句话说，这些态中的应力-能量张量在柯西视界上必然无法定义。 显示英文摘要

摘要： We show that an analogue of the (four dimensional) image sum method can be used to reproduce the results, due to Krasnikov, that for the model of a real massless scalar field on the initial globally hyperbolic region IGH of two-dimensional Misner space there exist two-particle and thermal Hadamard states (built on the conformal vacuum) such that the (expectation value of the renormalised) stress-energy tensor in these states vanishes on IGH. However, we shall prove that the conclusions of a general theorem by Kay, Radzikowski and Wald still apply for these states. That is, in any of these states, for any point b on the Cauchy horizon and any neighbourhood N of b, there exists at least one pair of non-null related points (x,x'), with x and x' in the intersection of IGH with N, such that (a suitably differentiated form of) its two-point function is singular. (We prove this by showing that the two-point functions of these states share the same singularities as the conformal vacuum on which they are built.) In other words, the stress-energy tensor in any of these states is necessarily ill-defined on the Cauchy horizon.