Is there a formula for such a thing?

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Discussion Overview

The discussion revolves around the concept of vacuum polarization in quantum field theory, specifically how vacuum fluctuations affect the effective charge of a nucleus and the implications for photon self-energy. Participants explore the theoretical framework and potential formulas related to these phenomena.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant describes a scenario where a nucleus with charge X is placed in a vacuum, questioning how vacuum polarization affects the measured charge at a distance R from the nucleus.
  • Another participant suggests that the "vacuum polarization tensor" is relevant, indicating that virtual particle pairs behave like dipoles in the presence of a charge, leading to screening effects.
  • A question is raised about whether a real photon can have self-energy, noting that photon splitting into an electron-positron pair would require energy from the Heisenberg uncertainty principle, leading to a discussion about the nature of virtual particles.
  • Further clarification is sought regarding self-energy as a quantum mechanical effect arising from particle interactions, with references to perturbation theory and Feynman diagrams.

Areas of Agreement / Disagreement

Participants express differing views on the nature of self-energy and the implications of vacuum polarization, indicating that the discussion remains unresolved with multiple competing perspectives on these concepts.

Contextual Notes

Limitations include the dependence on specific definitions of vacuum polarization and self-energy, as well as unresolved mathematical steps in the proposed scenarios.

Kruger
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Imagine following situation:

The whole space is in vacuum state.
We place in this space a nucleus with some charge X.
Now, there are everywhere vacuum fluctuations and thus the charge we measure near this nucleus is smaller than its effective charge (vacuum polarisation). Now, how big is this polarisation? I mean is there a formula we can calculate the charge we measure with a distance R apart from nucleus if the effective charge X of the nucleus is given?
 
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Kruger said:
Imagine following situation:

The whole space is in vacuum state.
We place in this space a nucleus with some charge X.
Now, there are everywhere vacuum fluctuations and thus the charge we measure near this nucleus is smaller than its effective charge (vacuum polarisation). Now, how big is this polarisation? I mean is there a formula we can calculate the charge we measure with a distance R apart from nucleus if the effective charge X of the nucleus is given?

If you are talking about how the physical vacuum influences real time interactions, than "vacuum polarization tensor" is the concept to look for. This tensor expresses the fact that if you replace the vacuum by a dielectric (this is the Dirac-virtual particle sea) that is built out of virtual electron positron pairs, these pairs will behave like ordinary dipoles if you introduce a charge. Plus, this charge will also get screened ofcourse.

regards
marlon
 
Another question:
Can a real photon have self energy? In the case of self energy a photon could split in an electron and a positron. But this is not possible. If this creation wants to be possible there most be energy taken from Heisenberg's uncertainty principle. But if so, the created electron and positron would not be real. So we would have a real photon at beginning and an intermediate state where all particles are virtual and then a final state where all particles (the photon) are real. Can't we then measure the e- and e+ created by the self energy of the real photon?
 
Kruger said:
Another question:
Can a real photon have self energy?

I do not understand this question. I mean, self energy is a purely QM effect that arises when there is some interaction between particles is going on. Keep in mind that self energy arises because of perturbationtheory, which is used for describing interactions. Yes a photon can interact with the Dirac sea (that is what the polarizationtensor is used for) and yes a photon can be converted (temporarily) into a electron-positron pair. I refer to the Feynman diagrams on http://www.oup.co.uk/pdf/0-19-852913-9.pdf

But keep in mind that we are looking at the interaction between a photon,positron and an electron.

marlon
 
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