Kähllén-Lehmann formula and MS scheme

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In summary, it is important to consider the differences between physical normalization conditions and the MS scheme when analyzing the electron self energy, as they may lead to different values for Z_2.
  • #1
eoghan
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Hi everybody!
Using "physical normalization conditions" I find for the electron self energy
[tex]
Z_2^{-1}=1-\frac{d\Sigma}{dp}(p=m)
[/tex]
where [itex]m[/itex] is the physical mass of the electron. Then [itex]Z_2[/itex] is the same constant appearing in the Kähllén-Lehmann representation (it is the residue at the pole of the physical propagator).
However, if I compute [itex]Z_2[/itex] in MS scheme, can I say that the [itex]Z[/itex] I found is not the same [itex]Z[/itex] in Kähllén-Lehmann?
 
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Hi there!

Thank you for sharing your findings on the electron self energy. It is always interesting to see different approaches and perspectives in the scientific community. In response to your question, it is important to note that the MS scheme is a different regularization scheme compared to physical normalization conditions. Therefore, the Z you found in MS scheme may not necessarily be the same Z in the Kähllén-Lehmann representation. However, both approaches have their own advantages and limitations, and it is up to the researcher to choose which one is more suitable for their specific study. I would recommend further exploring the differences between the two schemes and how they may affect your results. Keep up the great work!
 

1. What is the Kähllén-Lehmann formula?

The Kähllén-Lehmann formula is a mathematical formula used in quantum field theory to calculate the vacuum expectation value of a quantum field operator. It was developed by Swedish physicist Nils Kähllén and German physicist Gert Lehmann in the 1950s.

2. What is the MS scheme?

The MS scheme, short for minimal subtraction scheme, is a renormalization scheme used in quantum field theory to remove divergences from calculations. It was introduced by physicist Kenneth Wilson in the 1970s and is widely used in particle physics.

3. How are the Kähllén-Lehmann formula and MS scheme related?

The Kähllén-Lehmann formula is used in conjunction with the MS scheme to renormalize quantum field theory calculations. The formula is used to calculate the counterterms needed to remove divergences in the MS scheme, allowing for more accurate predictions of physical quantities.

4. What are the advantages of using the Kähllén-Lehmann formula and MS scheme?

The Kähllén-Lehmann formula and MS scheme are advantageous because they allow for the removal of divergences in quantum field theory calculations, making them more accurate and reliable. They also allow for the calculation of physical quantities that would otherwise be impossible to obtain due to the presence of divergences.

5. Are there any limitations to using the Kähllén-Lehmann formula and MS scheme?

While the Kähllén-Lehmann formula and MS scheme are widely used and have proven to be effective in removing divergences in calculations, they do have limitations. They are not applicable to all quantum field theories and may lead to inaccuracies in certain cases. Additionally, they require careful handling and may be computationally intensive.

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