In physics, an infrared divergence is a situation in which an integral, for example a Feynman diagram, diverges because of contributions of objects with very small energy approaching zero, or, equivalently, because of physical phenomena at very long distances.
The infrared (IR) divergence usually appears in theories with massless particles, and it means that we have asked an incorrect question. They represent a legitimate effect that a complete theory often implies. The correct treatment is to impose an infrared cutoff and refine the question.
See also ultraviolet divergence, cutoff, renormalization, renormalization group.