基于复变函数理论与电磁现象的基本规律，本文首先研究量子电动力学中传播子函数的洛伦兹协变形式并讨论传播子函数和推迟与超前格林函数之间的关系；其次利用傅里叶变换、常微分方程的性质结合边界条件导出推迟与超前格林函数；再次为波数添加无穷小虚部并将其应用于傅里叶变换，结合留数定理和(推广的)约当引理以更为严谨且简便的方式复现上述结果，并讨论了量子力学中非齐次薛定谔方程的因果格式函数；最后给出傅里叶-拉普拉斯积分定理的具体表述.以期为电动力学的教学研究提供一种新思路.

 Based on the theory of complex variable function and the basic laws of electromagnetic phenomena, the Lorentz invariant form of the propagator function in quantum electrodynamics is studied first, and the relationship between the propagator function and the delayed and advanced Green function is discussed. Secondly, the delayed and advanced Green's functions are derived by Fourier transform and the properties of ordinary differential equations combined with the boundary conditions. The infinitesimal imaginary part is added to the wave number again and applied to the Fourier transform. The result is reproduced in a more rigorous and simple way by combining the residue theorem and the equivalent lemma. Finally, the specific expression of the Fourier-Laplace integral theorem is given. It provides a new idea for the teaching and research of electrodynamics.