A question about the electron self-energy correction

[feld]

In QED, 'electron self energy' to first order results from an electron emitting and reabsorbing a photon.
But surely the emitted photon can be absorbed by any other electron in the universe, not just the emitting electron? Indeed it makes no sense to say the photon is absorbed by the same electron, because electrons are indistinguishable.
In other words, surely the feynman amplitude is going to be too large by a factor N, where N is the number of electrons the emitting electron can interact with?
Is the calculation guilty of isolating an electron-photon system from the rest of the universe?
Thoughts anyone?

 

[radium]

Rather than thinking of this as some scattering amplitude, you should think in terms of correlations functions (external legs are not on shell). To first order, the one in this case is just the bare electron propagator. Adding this self energy correction to get a new corrected propagator will change the location of the simple pole (the location of the pole is the physical electron mass, not the one in the Lagrangian). To higher orders you can have all sorts of things happen (for example you can sum it in a series, the photon progator may have corrections etc.).

 

[vanhees71]

What do you mean by "first order"? The usual QED self-energy diagram starts at 2nd order perturbation theory (two vertices, one loop).

The self-energy is defined as a correction to the single-electron propagator, i.e., it's a one-particle irreducible truncated two-point function. It's entering the higher-order corrections of S-matrix elements as "diagrammatic building block" in inner electron lines of a corresponding Feynman diagram.

 

[A. Neumaier]

In QED, 'electron self energy' to first order results from an electron emitting and reabsorbing a photon.

One cannot take the 1-loop Feynman diagram as the description of an actual process. If an electron emitted a photon, the latter would move away and never again come close enough to be reabsorbed. This is only a pictorial language, not something happening in reality. See “Misconceptions about Virtual Particles“