标题： 红外有限散射理论：散射态与BMS群的表示 显示英文标题

标题： Infrared finite scattering theory: Scattering states and representations of the BMS group

摘要： 在四维时空内，任何与无质量场的非平凡散射都会通常产生带有记忆的“出”态，这会在标准的$S$-矩阵中引发红外发散。 为了获得无红外发散的散射理论，必须适当地包含带有记忆的状态。 然而，除了带电粒子具有大质量的量子电动力学（QED）之外，对于更一般的理论（例如：无质量QED、杨-米尔斯理论和量子引力），尚未构建出能量和角动量有限的带有记忆的渐近态。 为此，我们在给定记忆的“洛伦兹轨道”上构建了直积分表示，并分类了所有具有明确能量和角动量的“轨道空间表示”。 我们从而提供了大量带有记忆的物理态的显式构造以及所有态的BMS荷的显式作用。 这类态的构造是制定无红外发散散射理论的关键步骤。 尽管我们的研究主要集中在量子引力方面，但我们概述了本文中提出的方法如何可以应用于更一般的量子场论以获得带有记忆的庞加莱群表示。 显示英文摘要

摘要： Any non-trivial scattering with any massless fields in four spacetime dimensions will generically produce an "out" state with memory which gives rise to infrared divergences in the standard $S$-matrix. To obtain an infrared-finite scattering theory, one must suitably include states with memory. However, except in the case of QED with massive charged particles, asymptotic states with memory that have finite energy and angular momentum have not been constructed for more general theories (e.g. massless QED, Yang-Mills and quantum gravity). To this end, we construct direct-integral representations over the "Lorentz orbit" of a given memory and classify all "orbit space representations" that have well-defined energy and angular momentum. We thereby provide an explicit construction of a large supply of physical states with memory as well as the explicit action of the BMS charges all states. The construction of such states is a key step toward the formulation of an infrared-finite scattering theory. While we primarily focus on the quantum gravitational case, we outline how the methods presented in this paper can be applied to obtain representations of the Poincar\'e group with memory for more general quantum field theories.