A question about the electron self-energy correction

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• feld
In summary: The self-energy correction is necessary because the photon emitted by the electron doesn't just disappear. It can interact with other particles in the universe, and the total energy of all those interactions is going to be larger than the energy of the original photon. In other words, the electron is going to emit a photon with a higher energy than the photon it originally emitted.This correction is called the electron self-energy, and it's first order in perturbation theory. In reality, higher-order corrections would add up and change the location of the simple pole, but at first order the self-energy just shifts the location of the pole by a fixed amount.The self-energy correction is just a building block
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?

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.).

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.

bhobba
feld said:
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

Last edited:
vanhees71

1. What is the electron self-energy correction?

The electron self-energy correction is a term in quantum field theory that takes into account the interactions of an electron with its own electric field. It is a correction to the mass and energy of an electron, and is important in understanding the behavior of particles in quantum systems.

2. Why is the electron self-energy correction important?

The electron self-energy correction is important because it helps us better understand the properties of electrons and other particles in quantum systems. It also plays a crucial role in calculations and predictions in quantum field theory and particle physics.

3. How is the electron self-energy correction calculated?

The electron self-energy correction is calculated using a mathematical technique called perturbation theory. This involves breaking down the interactions between the electron and its own electric field into smaller, more manageable parts that can be mathematically analyzed.

4. What effects does the electron self-energy correction have?

The electron self-energy correction has several effects, including changing the mass and energy of an electron, and affecting its interactions with other particles. It also plays a role in the phenomenon of vacuum polarization, where the electric field of an electron creates virtual pairs of particles in the vacuum.

5. Can the electron self-energy correction be observed experimentally?

Yes, the electron self-energy correction can be observed experimentally through precision measurements of the electron's properties, such as its mass and charge. These measurements must take into account the effects of the electron self-energy correction in order to accurately interpret the data.

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