Editing One-loop Feynman diagram (section)

{{Short description|Feynman diagram with only one cycle
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{{Use American English|date=January 2019}}{{Unreferenced|date=December 2009}}
{{Quantum field theory}}{{Toclimit|3}}
In [[physics]], a '''one-loop Feynman diagram''' is a [[connected component (graph theory)|connected]] [[Feynman diagram]] with only one [[cycle (graph theory)|cycle]] ([[unicyclic graph|unicyclic]]). Such a diagram can be obtained from a connected [[Feynman diagram|tree diagram]] by taking two external lines of the same type and joining them together into an edge.

Diagrams with loops (in graph theory, these kinds of loops are called [[cycle (graph theory)|cycles]], while the word [[loop (graph theory)|loop]] is an edge connecting a vertex with itself) correspond to the quantum corrections to the classical field theory. Because one-loop diagrams only contain one cycle, they express the next-to-classical contributions called the ''[[Semiclassical physics|semiclassical]] contributions''.

One-loop diagrams are usually computed as the [[integral]] over one independent momentum that can "run in the cycle". The [[Casimir effect]], [[Hawking radiation]] and [[Lamb shift]] are examples of phenomena whose existence can be implied using one-loop Feynman diagrams, especially the well-known "triangle diagram":

::[[Image:Triangle diagram.svg]]

The evaluation of one-loop Feynman diagrams usually leads to divergent expressions, which are either due to<ref>Peskin, M.E. Schroeder, D.V. (1995) ''An Introduction to Quantum Field Theory.'' CRC Press. ISBN 13: 978-0-201-50397-5</ref>:

* zero-mass particles in the cycle of the diagram ([[infrared divergence]]) or 
* insufficient falloff of the integrand for high momenta ([[ultraviolet divergence]]).

Infrared divergences are usually dealt with by assigning the zero mass particles a small mass ''λ'', evaluating the corresponding expression and then taking the limit <math>\lambda \to 0</math>.  Ultraviolet divergences are dealt with by [[renormalization]].