A type of divergence in quantum field theory that arises from massless particles with very low energy.Infrared divergence is a mathematical blow-up in quantum field theory that occurs when massless particles (like photons) are emitted with arbitrarily low energy. These divergences appear in calculations of scattering processes, threatening to make predictions infinite and meaningless. However, they are not physical catastrophes — they reflect the impossibility of detecting perfectly zero-energy particles and are resolved by summing over all possible undetectable emissions.
Infrared divergences were first identified in quantum electrodynamics in the 1930s by Felix Bloch and Arnold Nordsieck, who showed they cancel when accounting for soft photon emission. The full treatment was refined by others in the 1950s.
When a charged particle accelerates, it emits photons. In quantum calculations, you must sum over all possible photon emissions, including those with vanishingly small energy. The sum diverges logarithmically as photon energy approaches zero. The resolution, developed in the 1930s-50s, involves recognizing that any real detector has finite energy resolution, so you must include all emissions below that threshold. When done correctly, the divergences cancel, yielding finite, measurable predictions.
Understanding infrared divergences is essential for precise calculations in particle physics, such as predicting the properties of jets in collider experiments at CERN.
Infrared divergences are intimately connected to the fact that photons are massless — if photons had even a tiny mass, these infinities would vanish, but then the speed of light would depend on wavelength, contradicting observations.
