Contribution of vacuum fluctuation to the self-energy of the electron

In summary, Heitler's result for the energy of the electron due to vacuum fluctuations of the radiation field is only half of Weisskopf's result because Heitler's calculation only considers the transverse components of the electromagnetic field.
  • #1
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In the book" The Quantum Theory of Radiation", Heitler derived the transverse self-energy of the electron(Chapter III, Section18, Eq.(23))

$$\frac{{{e^2}}}{{\pi m}}\int_{\text{0}}^\infty {kdk} $$
which is the energy of the electron under the action of the vacuum fluctuation of the
radiation field. But it is one half of Weisskopf's result( (Phys. Rev. 56, 72,1939: page 81). Why? I can't figure it out.
 
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  • #2
Heitler's result is only one half of Weisskopf's result because Heitler's calculation only accounts for the transverse components of the electromagnetic field, while Weisskopf also considers the longitudinal components. Heitler's result comes from calculating the energy of the electron due to the transverse components of the electromagnetic field, while Weisskopf's result comes from calculating the energy of the electron due to both the transverse and longitudinal components of the electromagnetic field.
 

1. What is vacuum fluctuation?

Vacuum fluctuation refers to the spontaneous creation and annihilation of particle-antiparticle pairs in empty space. This phenomenon is a consequence of the uncertainty principle in quantum mechanics.

2. How does vacuum fluctuation contribute to the self-energy of the electron?

Vacuum fluctuation can lead to the creation of virtual particles, which can interact with the electron and affect its energy. This contribution to the electron's energy is known as the self-energy, and it is a result of the electron's interactions with the surrounding vacuum.

3. Why is the contribution of vacuum fluctuation to the self-energy of the electron important?

The self-energy of the electron is a fundamental property that affects its behavior and interactions with other particles. Understanding the contribution of vacuum fluctuation to the self-energy is crucial for accurately predicting and describing the behavior of electrons in various physical systems.

4. Can vacuum fluctuation affect the mass of the electron?

Yes, vacuum fluctuation can contribute to the mass of the electron through its effect on the self-energy. However, the overall mass of the electron is also influenced by other factors, such as its interactions with the Higgs field.

5. How is the contribution of vacuum fluctuation to the self-energy of the electron calculated?

The contribution of vacuum fluctuation to the self-energy of the electron is calculated using mathematical models and theories, such as quantum electrodynamics. These calculations involve considering the interactions between the electron and virtual particles in the surrounding vacuum.

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