July 16th, 2021

лошадь, диаграмма, Фейнман

Интегралы с бесселями - это всегда интересно :))

Alternative implementation of atomic form factors for dimuonium studies: https://arxiv.org/abs/2107.07392
Abdaljalel Alizzi, Abhijit Sen, Z.K. Silagadze
Using a new result on the integral involving the product of Bessel functions and associated Laguerre polynomials, published in the mathematical literature some time ago, we present an alternative method for calculating discrete-discrete transition form factors for hydrogen-like atoms. For comparison, an overview is also given of two other commonly used methods.
Comments: 14 pages, no figures
лошадь, диаграмма, Фейнман

Суммирование по поляризациям в КЭД и КХД, оптическая теорема и прочее

Using Covariant Polarisation Sums in QCD: https://arxiv.org/abs/2107.07187
M. Kachelriess, M.N. Malmquist
Covariant gauges lead to spurious, non-physical polarisation states of gauge bosons. In QED, the use of the Feynman gauge, ∑λϵ(λ)μϵ(λ)∗ν=−ημν, is justified by the Ward identity which ensures that the contributions of non-physical polarisation states cancel in physical observables. In contrast, the same replacement can be applied only to a single external gauge boson in squared amplitudes of non-abelian gauge theories like QCD. In general, the use of this replacement requires to include external Faddeev-Popov ghosts. We present a pedagogical derivation of these ghost contributions applying the optical theorem and the Cutkosky cutting rules. We find that the resulting cross terms A(c1,c¯1;…)A(c¯1,c1;…)∗ between ghost amplitudes cannot be transformed into (−1)n/2|A(c1,c¯1;…)|2 in the case of more than two ghosts. Thus the Feynman rule stated in the literature holds only for two external ghosts, while it is in general incorrect.
Comments: 9 pages, 3 pdf figures
лошадь, диаграмма, Фейнман

Как впарить паровую машину королю Неаполя и что из этого выйдет

From England to Italy: the intriguing story of Poli's engine for the King of Naples: https://arxiv.org/abs/2107.03062
Salvatore Esposito
An interesting, yet unknown, episode concerning the effective permeation of the scientific revolution in the XVIII century Kingdom of Naples (and, more generally, Italy) is recounted. The quite intriguing story of Watt's steam engine prepared for serving a Royal Estate of the King of Naples in Carditello reveals a fascinating piece of the history of that Kingdom, as well as an unknown step in the history of Watt's steam engine, whose final entrepreneurial success for the celebrated Boulton & Watt company was a direct consequence. That story unveils that, contrary to what claimed in the literature, the first introduction in Italy of the most important technological innovation of the XVIII century did not take place with the construction of the first steamship of the Mediterranean Sea, but rather 30 years before that, thanks to the incomparable work of Giuseppe Saverio Poli, a leading scholar and a very influential figure in the Kingdom of Naples. The tragic epilogue of Poli's engine testifies for its vanishing in the historical memory.
Comments: 25 pages, 6 figures
лошадь, диаграмма, Фейнман

Как постичь фрактальную размерность через настольные игры с сопротивлениями

Fractals on a benchtop: Observing fractal dimension in a resistor network: https://arxiv.org/abs/2107.02322
Charles E. Creffield
Our first experience of dimension typically comes in the intuitive Euclidean sense: a line is one dimensional, a plane is two-dimensional, and a volume is three-dimensional. However, following the work of Mandelbrot \cite{mandelbrot}, systems with a fractional dimension, ``fractals'', now play an important role in science. The novelty of encountering fractional dimension, and the intrinsic beauty of many fractals, have a strong appeal to students and provide a powerful teaching tool. I describe here a low-cost and convenient experimental method for observing fractal dimension, by measuring the power-law scaling of the resistance of a fractal network of resistors. The experiments are quick to perform, and the students enjoy both the construction of the network and the collaboration required to create the largest networks. Learning outcomes include analysis of resistor networks beyond the elementary series and parallel combinations, scaling laws, and an introduction to fractional dimension.