EVERY QFT text I've ever examined states that if there is an external vector potential, $A_\mu$, then one writes the Dirac eq.(or Klein-Gordon eq.) using a covariant derivative to include this U(1) gauge field, $A_\mu$. No problem. Wikipedia states that one must also include the contribution due to the electron self-field, $A_\mu'$. Again, makes perfect sense. Thus if there is no external 4-vector potential, the Dirac equation should exhibit the internal one! However, all texts state the "free" Dirac equation, without an accompanying vector potential.
If I now solve the free Dirac equation, the spinorial solutions can be used to construct the Dirac charged current. Using this current as the source, I can then solve the classical D'Alembertian eq. for the corresponding internal self-field $A_\mu'$.
If I insert $A_\mu'$ back into the Dirac equation, the solution must be different than those obtained from the free Dirac equation. I am simply wondering what the interpretation of the solutions will be now?