关键词: 传播子函数, 推迟格林函数, 超前格林函数, 傅里叶变换.

Abstract:  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.

Key words: propagation function, retarded Green function, advanced Green's function, Fourier transform