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
I am currently investigating an analogy between geodesic deviation from GR and the electromagnetic (Lorentz + Coulomb) force in QED. Once I got all the mathematical details worked out, I will make a thread about this, but I am tripping over the details of how to solve the classical Dirac equation perturbatively in a constant external EM field (mainly distribution-theoretical Fourier stuff). Does anyone here have a good reference on this?
Ethan Siegel just wrote an excellent blog about our new paper on Hawking radiation, giving a detailed explanation, why the event horizon is not necessary (and as usual he actually understands and explains some of these things better than I do!). Have a look - it saves me a long thread … https://bigthink.com/starts-with-a-bang/hawking-radiation-black-holes/