标题： Wightman 函数和脉冲平面波时空中的随机引力噪声核 显示英文标题

标题： Wightman function and stochastic gravity noise kernel in impulsive plane wave spacetimes

摘要： 在本文中，我们研究了在冲击平面波时空中的量子场论。 我们首先分析了这些时空中测地线和共轭平面的形成。 还考虑了世界函数和范维克行列式在共轭平面附近的性质。 对于量子场，我们求出了模函数、它们的布洛赫廖夫变换以及怀特曼函数的构造。 通过检查共轭平面上和附近的怀特曼函数，我们展示了当穿过该平面时，怀特曼函数的二重和四重奇异性结构是如何产生的。 最后，我们讨论了随机引力噪声核，这也是量子场应力能量张量的相关函数。 其显式形式是用世界函数和范维克行列式表示的。 我们研究了其在小和大测地线距离下的极限。 共轭平面上噪声核的主要发散项用δ函数的导数表示。 类似于怀特曼函数，我们还检查了当穿过共轭平面时，噪声核在光锥附近的奇异性结构如何变化。 显示英文摘要

摘要： In this paper we study quantum field theory in impulsive plane wave spacetimes. We first analyze the geodesics and the formation of conjugate planes in these spacetimes. The behaviors of the world function and the van Vleck determinant near conjugate plane are also considered. For the quantum field, we work out the mode functions, their Bogoliubov transformations, and the construction of the Wightman functions. By examining the Wightman function near and on the conjugate plane, we show how the twofold and fourfold singularity structure of the Wigthman function arise when crossing this plane. Lastly, we come to the stochastic gravity noise kernel which is also the correlation function of the stress energy tensor of the quantum field. Its explicit form is given in terms of the world function and the van Vleck determinant. We investigate its limits for small and large geodesic distances. The leading divergent term of the noise kernel on the conjugate plane are expressed in terms of derivatives of delta functions. Similar to that of the Wightman functions, we also examine how the singularity structure of the noise kernel near the lightcone changes when crossing the conjugate plane.