Infrared Divergence - Bremsstrahlung Example

Bremsstrahlung Example

When an electric charge is accelerated (or de-accelerated) it emits Bremsstrahlung radiation. Semiclassical electromagnetic theory, or the full quantum electrodynamic analysis, shows that an infinite number of soft photons are created. But only a finite number are detectable, the remainder, due to their low energy, falling below any finite energy detection threshold, which must necessarily exist. However even though most of the photons are not detectable they can't be ignored in the theory; Quantum electrodynamic calculations show that the transition amplitude between any states with a finite number of photons vanishes. Finite transition amplitudes are obtained only by summing over states with an infinite number of soft photons.