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I Interaction term in EM Lagrangian

  1. Nov 19, 2016 #1
    The (classical, relativistic) Lagrangian for electrodynamics contains the field energy density -FμνFμν/4 and the interaction term -Aμjμ. I understand the maths of that - for one thing, the equations of motion turn out right if you plug this into the Euler Lagrange equantion.
    Now I recall having learned that you can explain the forces between charged particles solely with the field energy: pushing 2 electrons together increases field energy because it goes with the square of the field strength, and pushing an electron and a positron together decreases field energy. If this is true, why do we need the interaction term at all? What am I missing?
  2. jcsd
  3. Nov 19, 2016 #2


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    If you do not have an interaction term, the charges do not generate a non-zero electromagnetic field.

    Furthermore, it is worth noting that you are considering the static limit when you are doing that type of calculation.
  4. Nov 19, 2016 #3
    Perfect answer, thanks! Makes me feel a bit stupid, though.
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