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 well-defined at very short distances.

The classic example of an ultraviolet divergence, and the scenario from which the name arises, occurs when one attempts to calculate the amount of radiation emitted by a black body using classical mechanics. As the wavelengths become shorter, there are more possible modes for the object to vibrate in. The calculation results in the object supposedly emitting infinite amounts of energy. This problem, which was known as the ultraviolet catastrophe, is addressed by quantum mechanics, which limits the amount of radiation emitted at low wavelengths by requiring that low-wavelength light exist in larger energy packets.

See also

• infrared divergence
• cutoff
• renormalization
• renormalization group