Editing Quantum electrodynamics (section)

===Mass renormalization===
{{Main|Self-energy}}

[[File:Electron self energy loop.svg|thumb|right|200px|[[Electron self-energy]] loop]]
A problem arose historically which held up progress for twenty years: although we start with the assumption of three basic "simple" actions, the rules of the game say that if we want to calculate the probability amplitude for an electron to get from ''A'' to ''B'', we must take into account ''all'' the possible ways: all possible Feynman diagrams with those endpoints.  Thus there will be a way in which the electron travels to ''C'', emits a photon there and then absorbs it again at ''D'' before moving on to ''B''. Or it could do this kind of thing twice, or more. In short, we have a [[fractal]]-like situation in which if we look closely at a line, it breaks up into a collection of "simple" lines, each of which, if looked at closely, are in turn composed of "simple" lines, and so on ''ad infinitum''. This is a challenging situation to handle. If adding that detail only altered things slightly, then it would not have been too bad, but disaster struck when it was found that the simple correction mentioned above led to ''infinite'' probability amplitudes. In time this problem was "fixed" by the technique of [[renormalization]]. However, Feynman himself remained unhappy about it, calling it a "dippy process",<ref name=feynbook/>{{rp|128}} and Dirac also criticized this procedure, saying "in mathematics one does not get rid of infinities when it does not please you".<ref name=":1" />