Electron positron pair density in charge renormalization

In summary, the conversation discusses the density of electron positron pairs surrounding a bare electron charge and the formula for calculating this density. The reference for vacuum polarization is Uehling's paper in Physical Review, which investigates the consequences of the positron theory for electrostatic fields. The formula for the induced charge is obtained by imposing a restriction on the maximum field intensity. The conversation also mentions the deviations from Coulomb's law and the displacement of energy levels for atomic electrons. The speaker is looking for a formula for the total amount of virtual pairs surrounding a charge, rather than just their net effect. However, this is considered a Frequently-Asked Meaningless Question as the modification of the Coulomb field is a result of a quantum superposition of any
  • #1
boger
2
0
I am trying to find out the density of electron positron pairs around a bare electron charge. In most texts, I saw that the treatment relates to the observed charge vs. the bare charge.
I wanted to know if there is a formula that describes the density of electron positron pairs that surround the electron or an estimate on the number of pairs that exist around it.
 
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  • #2
The standard reference for vacuum polarization is Uehling's paper in Physical Review: Phys. Rev. 48, 55–63 (1935)
Polarization Effects in the Positron Theory
Abstract
Some of the consequences of the positron theory for the special case of impressed electrostatic fields are investigated. By imposing a restriction only on the maximum value of the field intensity, which must always be assumed much smaller than a certain critical value, but with no restrictions on the variation of this intensity, a formula for the charge induced by a charge distribution is obtained. The existence of an induced charge corresponds to a polarization of the vacuum, and as a consequence, to deviations from Coulomb's law for the mutual potential energy of point charges. Consequences of these deviations which are investigated are the departures from the Coulombian scattering law for heavy particles and the displacement in the energy levels for atomic electrons moving in the field of the nucleus.
 
  • #3
Uehling paper on vacuum polarization refers to the change in the observed charge and the columb potential.
I am looking for a formula of the total amount of virtual pairs that surround a charge and not just their net effect. Anyone has an idea where to find such description?
 
  • #4
This is a FAMQ (Frequently-Asked Meaningless Question). Modification of the Coulomb field due to vacuum polarization results from a quantum superposition of any number of particle pairs.
 

1. What is electron positron pair density?

Electron positron pair density refers to the number of electron-positron pairs present in a given volume of space. These pairs are created through the process of charge renormalization, where the electric charges of particles are adjusted to account for the effects of virtual particles in quantum field theory.

2. How is electron positron pair density related to charge renormalization?

In charge renormalization, the electron positron pair density is used to calculate the strength of the electromagnetic interaction between particles. This is because the presence of virtual electron-positron pairs can affect the measured charge of a particle, and therefore need to be taken into account in calculations.

3. What factors affect the electron positron pair density in charge renormalization?

The electron positron pair density is affected by the energy scale of the system, the types and numbers of particles present, and the specific interactions between particles. In general, higher energy scales and larger numbers of particles lead to a higher pair density.

4. How is the electron positron pair density experimentally measured?

The electron positron pair density cannot be measured directly, as virtual particles are not observable. However, it is indirectly measured through experiments that test the predictions of quantum field theory, which incorporates charge renormalization. These experiments involve measuring the strength of the electromagnetic force between particles and comparing it to theoretical predictions.

5. How does the electron positron pair density affect the behavior of particles?

The electron positron pair density has a significant impact on the behavior of particles, especially at high energies. It affects the strength of the electromagnetic force between particles, which in turn can influence the stability and interactions of particles. Additionally, the presence of virtual particles can lead to slight deviations in the measured properties of particles, such as their mass and charge.

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