In physics, an ultraviolet divergence is a situation in which an integral, for example a Feynman diagram, diverges because of contributions of objects with very high energy (approaching infinity), or, equivalently, because of physical phenomena at very short distances. An infinite answer to a question that should have a finite answer is a potential problem. The ultraviolet (UV) divergences are often unphysical effects that can be removed by regularization and renormalization. If they cannot be removed, they imply that the theory is not perturbatively well-defined at very short distances.
The name comes from the earliest example of such a divergence, the "ultraviolet catastrophe" in understanding blackbody radiation. According to then-current theory of radiation, in this case, light, the quantity of energy released at any specific wavelength should increase with decreasing wavelength—that is, there should be considerably more ultraviolet light released from a blackbody radiator than infrared light. Measurements showed the opposite; the most energy was released at wavelengths between the two extremes, which suggested classic mechanics simply didn't describe the phenomenon correctly. This problem led to the development of quantum mechanics.
The success of the attack on the original ultraviolet catastrophe has led to the technique being widely applied in modern physics. A similar problem applying quantum field theory to electromagnetism was famously solved through the use of renormalization groups and the successful creation of quantum electrodynamics (QED). Similar techniques led to the modern standard model of particle physics. Ultraviolet divergences remain a key process in the exploration of new physical theories, like supersymmetry.
A successful attack on an ultraviolet divergence is known as ultraviolet completion.
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