Re:Why Feynman Diagrams Are So Important
by solaris999 on Thursday July 07, 2016 @06:48AM
(#12048534)
I heard a good rule of thumb to follow when drawing Feynman Diagrams is that the fewer lines there are, the more probable the occurrence of the event represented by the diagram. So at the simplest case, a single line representing an unchanging particle, is far far more likely than any two particle interactions (3 lines) and so on.
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This is true if the system you're trying to describe is weakly coupled.
If the theory is strongly coupled, then in fact more and more complicated diagrams count more and more. In this case the method of Feynman diagrams because basically useless---in the case you describe you know you can get most of the answer from a simple calculation (of the simplest diagrams). But if more complicated diagrams count more (as in strong coupling) then you don't have a place to start, because whatever diagram you pick to start at I can make more complicated and be confident that my new diagram counts more than the pieces you've computed.
In that case we need a different approach, the most generic of which is lattice field theory
https://en.wikipedia.org/wiki/Coupling_constant#Weak_and_str...
Roughly, though it is actually the number of vertices and depends on the particles involved (obviously a diagram representing something very unlikely is less likely than some normal process)