4 ms·

Can those Feymann diagrams be calculated by a computer? I understand that it raises expotentially, but why the 891 and 320 thousand diagrams cannot be solved by

• evanb 4y ago
  Yes, but you very quickly run out of steam. Moreover, we know the perturbative series does not converge for many theories. For QED, for example, the radius of convergence must be 0, by an argument due to Dyson. Roughly: 1. The perturbative series is an analytic function of the fine structure constant α, which is proportional to the electron charge squared. 2. Like charges repel and therefore α>0. If like charges attracted the vacuum would be unstable against the continuous creation of electron-positron pairs from the vacuum and the electrons going to one part of the universe and the positrons to the other. 3. Because of this instability the series converges for no α<0, and since the perturbative expansion is analytic in α cannot converge for any α>0 either.
• yunruse 4y ago
  Of course! But the R&D for those tools are very peculiar, at least as I understand it from a friend who works directly on this domain. Essentially there are a whole variety of different interactions, some of them which interact with themselves. You wind up with a tiny zoo of bizarre diagrammatic creatures that you have to figure out herding patterns for - and only then can you get the tool to do the herding for you. I seem to remember involved a whole deal of abstract group theory. It's way easier to draw the diagrams on paper to solve all cases of an interaction, anyhow; after all that nightmare you wind up with some result. And from what I recall, the number of cases also grows exponentially too D: