= Infrared divergence
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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.
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