# Action corresponding to photon emission

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1. Nov 7, 2014

### semc

Hi I am trying to write the probability of photon emission due to transition of electron in feynman's path integral formulation. I am stuck trying to figure out the action corresponding to the photon emission. Would anyone shed some light on this? Thanks

2. Nov 7, 2014

### jjustinn

If I'm not mistaken (and I could very well be, as I'm a dilettante dabbler), the corresponding 1st-order diagram would be an incoming electron with momentum p, and an outgoing electron with a momentum (p-k) and photon with momentum k, so the perturbation expansion term would have a destruction operator for the electron with momentum p, and the electron/photon creation operators with momenta (p-k)/k.

However, if you're asking about the actual action S corresponding to that situation, as in the integral over a term in the Lagrangian, I don't think there is one; the "electron emitting a photon" and all of the other possibilities come from the perturbation expansion of the (exponential of?) the normal, (semi-)classical action, where the only term giving the interaction between the electron field and the Maxwell field is just the minimal-coupling term ($j_{\mu} A^{\mu}$?); everything else derives from that.

But, again, caveat emptor.