Infrared divergence refers to a type of divergence that occurs in quantum field theory (QFT) and certain fields of theoretical physics when dealing with low-energy (or long-wavelength) phenomena. Specifically, it manifests when evaluating Feynman integrals or loop diagrams that include virtual particles with very low momenta (approaching zero). In such scenarios, the contributions from these low-energy states can lead to integrals that diverge, meaning they yield infinite values.
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An infrared divergence arises from contributions at arbitrarily low energy or long wavelength. A massless mode can produce such a problem because many soft excitations are available at very small energy, or because a long-distance fluctuation integral fails to converge.
Its interpretation depends on the observable. In scattering, an exclusive amplitude with no additional arbitrarily soft radiation need not be separately measurable; combining appropriately inclusive real-emission and virtual contributions can remove the relevant divergence. In equilibrium field theory, an infrared-divergent order parameter fluctuation can instead diagnose failure of an assumed ordered-state approximation. A finite size or detector resolution may regulate the calculation, but the dependence on that regulator must be interpreted rather than silently discarded.