超强激光技术的发展给众多学科领域带来了深远的影响，也给强场量子电动力学研究提出了新的问题，最主要的挑战是如何从量子电动力学基本原理出发,研究强电磁场环境中光和物质的非微扰相互作用。对于平面波场，已经发展出激光缀饰QED方法，但对于一般构型的非平面波场，例如与实验紧密相关的聚焦场、多光束汇聚场等，理论研究遇到了一系列瓶颈问题，限制了对实验的解释和发现新物理问题的能力。本项目将突破原有理论和技术的局限，发展高效求解量子力学Klein-Gordon方程和Dirac方程的理论和数值方法，细致研究非平面波强场中粒子的量子动力学，在此基础上建立具有清晰物理图像和严格数学推导的处理非平面波强电磁场中散射问题的非微扰理论和计算方法，来解决不限构型的强场中量子电动力学问题，包括激光诱导康普顿散射、激光诱导正负电子对产生和激光辅助韧致辐射，深入理解强场量子物理现象，为下一步实验发展提供可靠的预测和对比数据。

The development of strong laser technology has a fundamental influence on many research areas, and poses new questions to the strong-field quantum electrodynamics research. The main theoretical challenge is to develop new methods based on the fundamental quantum electrodynamics principles to study the nonperturbative light-matter interaction in a strong electromagnetic field. As for a plane-wave field, a laser-dressed QED method has been developed, but for a general non-plane-wave field, such as a focused field or a multi-beam-colliding field with especially experimental relevance, a series of bottleneck problems are encountered in theoretical study, which hinders the theoretical ability to explain the measured results and discover new physical problems. In this project, it is intended to make a breakthrough in the theory and techniques, by developing theoretical and numerical methods to effectively solve the Klein-Gordon equation and Dirac equation, studying the quantum dynamics in non-plane-wave fields in detail, and on this basis constructing non-perturbative theoretical and numerical methods with a clear physical picture and mathematical rigor to solve the scattering problem in a non-plane-wave strong field. In this way, strong field electrodynamics problems can be explored without constraints on the configuration of the field. Laser-induced Compton scattering, laser-induced pair production and laser-assisted bremsstrahlung will be studied, in order to offer deeper insights in the strong field quantum physics, and provide prediction as well as comparison data for experiments in the future.