I am referring to quantum field theory, if electron is excitation in the electron field then can't these excitations interact with each other like the ripples on a pond? I find it weird that the electron field need to transfer energy through a different field just to interact on itself, maybe it's just me.
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3 Answers
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Actually if you integrate out the photon fields you have an electron field interacting with itself. Just different mathematical formulations for the same physics.
It just seems to be easier to deal with electrons (weakly) interacting with each other through an intermediary field.
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It's more about academic categories than reality. "Force" in QFT has evolved to have an entirely different meaning than "the thing a force gauge measures". But the Pauli force that keeps you from falling through the floor is a real, physical force between electrons.
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if electron is excitation in the electron field then can't these excitations interact with each other like the ripples on a pond?
Model with QFT an electron of constant velocity moving in vacuum. You will need continual creation-annihilation operators , operating on the electron field to model the motion.It is an excitation at a specific (x,y,z,t) , and will be de-excited and the next (x,y,z,t) will be excited, so there are no excitations next to each other at the same time t.
