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Bob_for_short
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Is there any solution ψ to understand how the real electron looks like after renormalization (dressing)?
meopemuk said:In the "dressed particle" approach to QED, the electron is simply a point (structureless) particle with usually measured mass and charge.
Bob_for_short said:And according to QED, the external lines have no corrections after all. So the effect of renormalization (dressing) boils down to zero, doesn't it?
Bob_for_short said:And according to QED, the external lines have no corrections after all. So the effect of renormalization (dressing) boils down to zero, doesn't it?
meopemuk said:Yes, the electron self-energy (or electron mass renormalization) counterterm cancels exactly the contribution coming from electron-photon loops attached to external electron lines. So, in renormalized QED, there is no need to draw loops in external electron lines.
However, the electron self-energy counterterm does not cancel loops in internal electron lines, because these lines are "not on the mass shell". The residual terms are responsible for small radiative corrections.
Though, I am not sure how this question is related to your previous one (about the dressed electron).
Bob_for_short said:If the free (incident and scattered) particles are the same after renormalizations, that means only interaction Hamiltonian modification (removing self-interaction) in course of perturbative renormalizations. What sense to speak of dressed or renormalized particles if they are the same?
meopemuk said:All these problems can be fixed in the "dressed particle" approach, where the Hamiltonian of QED (with renormalization counter-terms) is modified (via an unitary transformation that preserves the scattering matrix) so that self-interaction terms get removed. Then the difference between "bare" and "dressed" particles disappears. The theory is formulated in terms of real observable particle states. Another good thing is that it is guaranteed (by construction) that the scattering matrix in the "dressed" approach is exactly the same as in the renormalized QED, i.e., agrees with experiment very well.
Bob_for_short said:Thank you, Eugene, for your exhaustive explanation. I wonder if on can start from the modified Hamiltonian (without self-action term) from the very beginning rather than modify it perturbatively?
Too bad, they are there with clear physical and mathematical motivations.meopemuk said:Yes, it should be possible, in principle. However, there are two major difficulties. First, how are you going to derive this modified Hamiltonian? From which principles? Second, you need to demonstrate that this Hamiltonian describes correctly already known scattering processes and spectra (e.g., the Lamb shift). I couldn't find answers to these questions in your works.
So where are your results on scattering and the Lamb shift?meopemuk said:On the other hand, in the usual "dressed particle" approach these questions have satisfactory answers. The "dressed particle" Hamiltonian is derived by applying an unitary transformation to the Hamiltonian of the standard renormalized QED. The unitarity of this transformation guarantees that the scattering matrix of the "dressed" approach is exactly the same as the scattering matrix of the orthodox renormalized QED. I.e., it agrees with experiment very well. Eugene.
Bob_for_short said:So where are your results on scattering and the Lamb shift?
QED stands for Quantum Electrodynamics, which is a theory that explains the behavior of electrons and photons in the quantum realm. It is a fundamental theory in physics that combines quantum mechanics and special relativity.
According to QED, electrons are surrounded by a cloud of virtual particles (photons) that constantly interact with them. This interaction changes the properties of the electron, giving it an effective mass and charge, making it appear "dressed".
A dressed electron is an electron that is surrounded by a cloud of virtual particles, which changes its properties and makes it appear as if it has a different mass and charge than it actually does. This is a result of the constant interaction between the electron and the virtual particles in the quantum realm.
No, we cannot directly observe a dressed electron because it is a quantum phenomenon that occurs on a very small scale. However, we can indirectly observe its effects through experiments and calculations using QED.
In QED, the dressed electron does not have a physical appearance as it is a theoretical concept. It is a mathematical description of the electron's behavior in the quantum realm, taking into account the interactions with virtual particles. Therefore, it is not possible to visualize or describe the appearance of a dressed electron in QED.