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 relation-ship between the propagator function and the delayed and advanced Green function is discussed.Secondly,the de-layed 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 combi-ning 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.
propagation functionretarded Green functionadvanced Green's functionFourier transform
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