Infrared divergence

In physics, an infrared divergence (also IR divergence or infrared catastrophe) 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.

Overview

The infrared divergence only appears in theories with

photons

, the energy is given by

E=h\nu

, where

\nu

is the frequency associated to the particle and as it goes to zero, like in the case of

infrared cutoff

and take the limit as the cutoff approaches zero and/or refine the question. Another way is to assign the massless particle a fictitious mass, and then take the limit as the fictitious mass vanishes.

The divergence is usually in terms of particle number and not empirically troubling, in that all measurable quantities remain finite.

UV catastrophe

where the energies involved diverge.)

Bremsstrahlung example

When an

transition amplitude between any states with a finite number of photons vanishes. Finite transition amplitudes are obtained only by summing over states with an infinite number of soft photons.^[1]^[2]

The zero-energy photons become important in analyzing the

Bremsstrahlung radiation in the coaccelerated frame in which the charge experiences a thermal bath due to the Unruh effect. In this case, the static charge will only interact with these zero-energy (Rindler) photons in a sense similar to virtual photons in the coulomb interaction.^[3]^[4]