Bound-State Relativistic Quantum Electrodynamics: A Perspective for Precision Physics with Atoms and Molecules

Precision physics aims to use atoms and molecules to test and develop the fundamental theory of matter, possibly beyond the Standard Model. Most of the atomic and molecular phenomena are described by the quantum electrodynamics (QED) sector of the Standard Model. Do we have the computational tools, algorithms, and practical equations for the most possible complete computation of atoms and molecules within the QED sector? What is the fundamental equation to start with? Is it still Schrödinger’s wave equation for molecular matter, or is there anything beyond that? This paper provides a concise overview of the relativistic QED framework and recent numerical developments targeting precision physics and spectroscopy applications with common features of the robust and successful relativistic quantum chemistry methodology.精密物理（Precision physics）旨在借助原子与分子，检验并发展物质的基础理论，甚至有望突破标准模型（Standard Model）的范畴。绝大多数原子与分子现象均可通过标准模型中的量子电动力学（quantum electrodynamics, QED）领域加以描述。那么，我们是否已掌握可在QED领域内实现原子与分子最完备计算所需的计算工具、算法与实用方程？我们应当以何种基础方程作为研究起点？是沿用针对分子体系的薛定谔波动方程（Schrödinger's wave equation），还是存在更为前沿的替代方案？本文面向精密物理与光谱学应用场景，结合成熟稳健且成效显著的相对论量子化学（relativistic quantum chemistry）方法论的共性特征，对相对论性QED框架及最新数值计算进展展开了简要综述。