Why we do not consider the divergence due to mass-shell in QED?

In summary, the mass-shell divergence is not considered in QED because it is a mathematical artifact that is cancelled out in the renormalization process. It arises from the use of virtual particles in perturbation theory, but does not affect the physical predictions of QED. While it cannot be completely eliminated, there are alternative theories that avoid it, but they are more complex and computationally challenging.
  • #1
ndung200790
519
0
Please teach me this:
Why we do not consider the divergences in loops in QED when p[itex]^{2}[/itex]→m[itex]^{2}[/itex] but only consider the soft photon when k[itex]^{2}[/itex]→0(IR divergence) and UV divergence?
Thank you very much in advance.
 
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  • #2
p²-m² is always regulated via the "iε-Term" and is evaluated via the Cauchy contour integral
 
  • #3
Why we have not the same consideration when m=0?
 
  • #4
Sorry,Now I have understood.Applying Cauchy's theorem when m=0(so k[itex]^{2}[/itex]→0)
we have divergence(IR divergence)
 

1. Why is the mass-shell divergence not considered in QED?

The mass-shell divergence is not considered in QED because it is a mathematical artifact that arises due to the use of perturbation theory in calculations. While it may appear to be a problem at first, it is actually accounted for and cancelled out in the renormalization process, which is a crucial step in QED calculations.

2. What is the origin of the mass-shell divergence in QED?

The mass-shell divergence in QED arises from the use of virtual particles in perturbation theory. These virtual particles have infinite mass and energy, which leads to the divergence. However, these virtual particles are not observable and are only used as mathematical tools in calculations.

3. Does the mass-shell divergence affect the physical predictions of QED?

No, the mass-shell divergence does not affect the physical predictions of QED. As mentioned earlier, it is accounted for and cancelled out in the renormalization process. The final physical predictions of QED are free from any infinities or divergences.

4. Can the mass-shell divergence be completely eliminated in QED?

No, the mass-shell divergence cannot be completely eliminated in QED. It is an inherent part of the mathematical framework used in perturbation theory. However, as mentioned earlier, it is accounted for and cancelled out in the renormalization process, leading to finite and accurate physical predictions.

5. Are there any alternative theories that avoid the mass-shell divergence in QED?

Yes, there are alternative theories, such as the lattice QED, that avoid the mass-shell divergence in QED. These theories use a different mathematical approach and do not rely on perturbation theory. However, they are more complex and computationally challenging, and the results obtained are equivalent to those of QED in most cases.

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