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Simple question about QED

This is a layman.  I have a question about Feynman diagram.  The Feynman diagram depicts an interaction between  two electrons in a way in which one electron emits a photon and then after a little time the other electron receives and absorbs that photon.

The question that I would like to ask is this.

How can an electron generate and emit a photon? Does an electron have its internal structure in which some kind of electromagnetic wave-generating device is involved?  What sort of event triggers the emission of a photon?  The QED (Quantum Electro Dynamics) theory does not explain the mechanism of such a photon emission or  photon absorption by an electron.

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Re: Simple question about QED

What I am wondering is this.

To me, the concept of the exchange of photon that the QED theory says can explain the interaction between two electrons, seems to lack its foundation, and seems to be almost ad hoc and dogmatic.  Is the concept of exchange of photon well established?  Don't you have any doubt on that theory?  Can anybody show me the calculation that starts from the equations that describe the echange of photon to the equation of Coulomb's law of inverse squared force between two electrons?

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