In #QuantumFieldTheory, scattering amplitudes can be computed as sums of (very many) #FeynmanIntegral s. They contribute differently much, with most integrals contributing near the average (scaled to 1.0 in the plots), but a "long tail" of integrals that are larger by a significant factor.
We looked at patterns in these distributions, and one particularly striking one is that if instead of the Feynman integral P itself, you consider 1 divided by root of P, the distribution is almost Gaussian! To my knowledge, this is the first time anything like this has been observed. We only looked at one quantum field theory, the "phi^4 theory in 4 dimensions". It would be interesting to see if this is coincidence for this particular theory and class of Feynman integrals, or if it persists universally.
More background and relevant papers at https://paulbalduf.com/research/statistics-periods/ #quantum#physics#statistics
@paulbalduf - that's a great observation! Have you written a paper about it? It's worthwhile, even if it's only true for the ϕ₄⁴ theory. Which class of Feynman diagrams were you considering? E.g. 4-point functions?
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