Photon-based spectroscopies have had a significant impact on both fundamental science and applications by providing an efficient approach to investigate the microscopic physics of materials. Together with the development of synchrotron X-ray techniques, theoretical understanding of the spectroscopies themselves and the underlying physics that they reveal has progressed through advances in numerical methods and scientific computing. In this Review, we provide an overview of theories for angle-resolved photoemission spectroscopy and resonant inelastic X-ray scattering applied to quantum materials. First, we discuss methods for studying equilibrium spectroscopies, including first-principles approaches, numerical many-body methods and a few analytical advances. Second, we assess the recent development of ultrafast techniques for out-of-equilibrium spectroscopies, from characterizing equilibrium properties to generating transient or metastable states, mainly from a theoretical point of view. Finally, we identify the main challenges and provide an outlook for the future direction of the field.

通过提供一种有效的方法来研究材料的微观物理学，基于光子的光谱学对基础科学和应用都产生了重大影响。随着同步加速器X射线技术的发展，通过数值方法和科学计算的进步，对光谱学本身及其揭示的基本物理学的理论理解也得到了发展。在这篇综述中，我们概述了应用于量子材料的角度分辨光发射光谱和共振非弹性X射线散射的理论。首先，我们讨论用于研究平衡光谱的方法，包括第一性原理方法，数值多体方法和一些分析进展。第二，我们主要从理论角度评估从平衡性质表征到产生瞬态或亚稳态的超快光谱技术用于不平衡光谱学的最新进展。最后，我们确定了主要挑战，并对该领域的未来方向提供了展望。