# Furry's theorem and soft bremsstrahlung

• Einj
In summary, the conversation discusses Furry's theorem, which states that diagrams with an odd number of photons vanish due to charge conjugation symmetry. However, the "soft bremsstrahlung" diagram, which involves e+e- scattering with an additional photon, does not vanish and is used to deal with infrared divergences in QED. This is because Furry's theorem only applies when an odd number of photons are connected to the same internal fermion loop.
Einj
Hi everyone, I have a doubt which was actually raised by a recent discussion on this forum.
We know that Furry's theorem says that diagrams with an odd number of photon vanish. Roughly the reason behind that is the charge conjugation symmetry, since under such operation the photon field behaves like $A_\mu\to -A_\mu$.

However, I have seen many times the "soft bremsstrahlung" diagram, i.e. e+e- scattering with the emission of an additional photon. This diagram is usually used to deal with infrared divergences in QED. Why doesn't it vanish?

Thank you very much.

As was said in that thread, Furry's Theorem applies only when an odd number of photons is connected to the same internal fermion loop.

Let's not discuss this in two places.

## 1. What is Furry's theorem?

Furry's theorem is a mathematical principle that relates the symmetry properties of particles to their interactions with electromagnetic fields. It states that the scattering amplitude for a particle with spin j and magnetic moment μ in an external electromagnetic field is proportional to the product of j and μ.

## 2. How does Furry's theorem relate to soft bremsstrahlung?

Furry's theorem is used in the calculation of soft bremsstrahlung, which is a type of electromagnetic radiation emitted when charged particles are accelerated. The theorem helps to determine the probability of a charged particle emitting a photon during this process.

## 3. What is soft bremsstrahlung?

Soft bremsstrahlung is a type of low-energy electromagnetic radiation that is emitted when charged particles are accelerated. It is commonly observed in high-energy physics experiments and is an important phenomenon to consider in particle interactions.

## 4. How is Furry's theorem applied in practical experiments?

Furry's theorem is used in the calculation of scattering amplitudes and cross-sections in high-energy physics experiments. It is also used in theoretical models to predict the behavior of particles in an external electromagnetic field.

## 5. Are there any limitations to Furry's theorem?

While Furry's theorem is a useful tool in theoretical calculations, it does have its limitations. It assumes that the external electromagnetic field is weak and that the particles involved have spin and magnetic moment. It also does not take into account other interactions, such as strong and weak nuclear forces.

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