论文标题
全球双曲机空间上的全球波参数
Global wave parametrices on globally hyperbolic spacetimes
论文作者
论文摘要
在最近的一项工作中，第一位命名的作者列维汀和Vassiliev在封闭的Riemannian歧管$ M $上构建了波传播器，作为一个单个振荡性的整体全球全球，并及时使用杰出的复杂值值相位函数。在本文中，首先，我们用超级洛伦兹歧管的语言自然地重新解释了基本算法结构。随后，我们证明，由于对超级方案的适当减少，该构造将延伸到静态背景的情况下。最后，我们证明可以将整个过程推广到具有紧凑的cauchy表面的任何全球双曲线时空。作为一个应用程序，我们讨论如何从我们的过程中恢复局部HADAMARD扩展，该扩展在曲面背景上的量子场理论中在所有应用中都起着关键作用。
In a recent work the first named author, Levitin and Vassiliev have constructed the wave propagator on a closed Riemannian manifold $M$ as a single oscillatory integral global both in space and in time with a distinguished complex-valued phase function. In this paper, first we give a natural reinterpretation of the underlying algorithmic construction in the language of ultrastatic Lorentzian manifolds. Subsequently we show that the construction carries over to the case of static backgrounds thanks to a suitable reduction to the ultrastatic scenario. Finally we prove that the overall procedure can be generalised to any globally hyperbolic spacetime with compact Cauchy surfaces. As an application, we discuss how, from our procedure, one can recover the local Hadamard expansion which plays a key role in all applications in quantum field theory on curved backgrounds.
