# What is the connection between the Lamb Shift and the g factor?

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• raracon
In summary, the German Wikipedia mentions that the g factor is connected to the Lamb Shift through the radiative corrections of the e\bar{e}\gamma vertex function. Without these corrections, the anomalous g factor would not occur and the Lamb Shift would not be affected.
raracon
TL;DR Summary
Trying to find a connection between these two (Lamb Shift and G factor aka anomalous magnetic moment)
German Wikipedia mentions that the g factor is one of the causes of the Lamb Shift. It does not say why and I am trying to find a connection between these two things. Any ideas?

The anomalous ##g## factor (devisions from 2 for elementary Dirac particles like the electron or muon) are due to the radiative corrections of the ##e\bar{e}\gamma## vertex function, which are also contributing to the Lamb shift of the hydrogen-atom levels.

vanhees71 said:
The anomalous ##g## factor (devisions from 2 for elementary Dirac particles like the electron or muon) are due to the radiative corrections of the ##e\bar{e}\gamma## vertex function, which are also contributing to the Lamb shift of the hydrogen-atom levels.
Ah I see. And how are they contributing? What would change if they would not be there?

## 1. What is the Lamb Shift?

The Lamb Shift is a tiny energy difference between two energy levels in the hydrogen atom, first observed by Willis Lamb and his colleagues in 1947. It is caused by the interaction between the electron and the quantum fluctuations of the vacuum.

## 2. What is the g factor?

The g factor, also known as the Landé g factor, is a dimensionless quantity that describes the magnetic moment of a particle or atom. It is a measure of how much the particle's spin or orbital angular momentum responds to an external magnetic field.

## 3. What is the connection between the Lamb Shift and the g factor?

The connection between the Lamb Shift and the g factor lies in the fact that the Lamb Shift is caused by the interaction between the electron and the quantum fluctuations of the vacuum, which in turn affects the electron's spin and orbital angular momentum. This results in a small change in the g factor, which can be measured experimentally.

## 4. How does the g factor affect the Lamb Shift?

The g factor affects the Lamb Shift by causing a small change in the energy levels of the hydrogen atom. This change is due to the interaction between the electron and the quantum fluctuations of the vacuum, which in turn affects the electron's spin and orbital angular momentum. The resulting change in the g factor can be measured as a tiny difference in the energy levels of the atom.

## 5. Why is the study of the Lamb Shift and the g factor important?

The study of the Lamb Shift and the g factor is important because it helps us understand the fundamental properties of matter and the quantum nature of the universe. It also has practical applications in fields such as atomic and molecular physics, quantum mechanics, and precision measurements. Additionally, the Lamb Shift and the g factor have been extensively studied and tested, providing evidence for the validity of quantum electrodynamics, one of the most successful theories in modern physics.

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