Furry's theorem and soft bremsstrahlung

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Furry's theorem states that diagrams with an odd number of photons vanish due to charge conjugation symmetry, where the photon field changes sign. However, the "soft bremsstrahlung" diagram, which involves e+e- scattering with an additional photon, does not vanish because it connects to different internal fermion loops rather than a single loop. This distinction allows the soft bremsstrahlung process to be relevant in addressing infrared divergences in quantum electrodynamics (QED). The discussion emphasizes the importance of understanding the specific conditions under which Furry's theorem applies. Clarifying these points helps resolve the apparent contradiction regarding photon emissions in particle interactions.
Einj
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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.
 
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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.
 

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