标题： 静态弯曲时空中的量子力学路径积分与热辐射 显示英文标题

标题： Quantum mechanical path integrals and thermal radiation in static curved spacetimes

摘要： 我们从静态弯曲时空（具有事件视界）的量子力学路径积分形式论出发，计算了一个无自旋粒子的传播子。考虑了一个玩具模型——Gui时空以及二维和四维施瓦西黑洞。在此框架下，强调了坐标构型空间拓扑的作用。为了用单一坐标系覆盖上述时空，我们将“托罗什坐标”推广到复数值。结果显示，复数托罗什构型空间的同伦性质意味着这些时空中传播子的热行为。当端点位于由一个或多个事件视界分隔的相同或不同时空区域时，传播子被计算出来。证明了在第五变量下，通过事件视界的量子演化是幺正的。 显示英文摘要

摘要： The propagator of a spinless particle is calculated from the quantum mechanical path integral formalism in static curved spacetimes endowed with event-horizons. A toy model, the Gui spacetime, and the 2D and 4D Schwarzschild black holes are considered. The role of the topology of the coordinates configuration space is emphasised in this framework. To cover entirely the above spacetimes with a single set of coordinates, tortoise coordinates are extended to complex values. It is shown that the homotopic properties of the complex tortoise configuration space imply the thermal behaviour of the propagator in these spacetimes. The propagator is calculated when end points are located in identical or distinct spacetime regions separated by one or several event-horizons. Quantum evolution through the event-horizons is shown to be unitary in the fifth variable.