An ultraviolet divergence comes from arbitrarily large loop momentum, equivalently from singular short-distance behavior. Locality makes its regulator dependence cancellable by local counterterms in a renormalizable theory.
An ultraviolet subdivergence arises when loop momenta internal to a proper subgraph tend to infinity while the momenta entering that subgraph are held fixed. It can occur even if simultaneous scaling of all momenta of the full Feynman diagram is convergent. Recursive local counterterms subtract these subgraph divergences before the remaining overall divergence is analyzed. A tadpole diagram inserted into an otherwise convergent six-point phi-fourth theory Feynman diagram is a simple massive example.
Articles by others on the same topic
Ultraviolet (UV) divergence is a concept in quantum field theory and quantum mechanics that refers to the phenomenon where certain integrals, especially those that arise in the calculation of particle interactions and vacuum fluctuations, yield infinite results when evaluated at high energy (or short distance) scales. This is particularly relevant in theories like quantum electrodynamics (QED) and quantum chromodynamics (QCD), where loop diagrams (representing virtual particles) can produce divergences.