Divergences

Loop diagrams in QED can produce integrals that diverge—at high momenta (ultraviolet), at low momenta (infrared), or not at all. The divergence structure of a diagram determines how it must be treated: renormalized, summed with real emission processes, or computed directly.

UV Ultraviolet divergence

An ultraviolet (UV) divergence arises when a loop integral receives unbounded contributions from arbitrarily high momenta — equivalently, arbitrarily short distances. The...

9 diagrams

IR Infrared divergence

An infrared (IR) divergence arises when loop integrals receive unbounded contributions from arbitrarily low momenta — arbitrarily long distances. In QED this happens because...

5 diagrams

finite Finite diagrams

A finite diagram has no ultraviolet or infrared divergences — the loop integrals converge at both high and low momenta, giving a well-defined numerical result without regularization.

14 diagrams