June 19th, 2019

лошадь, диаграмма, Фейнман

Полезная методическая статья о перенормировках

Renormalons in quantum mechanics: https://arxiv.org/abs/1906.07198

We present a nonrelativistic one-particle quantum mechanics whose perturbative S-matrix exhibits a renormalon divergence that we explicitely compute. The potential of our model is the sum of the 2d Dirac δ-potential -- known to require renormalization -- and a 1d Dirac δ-potential tilted at an angle. We argue that renormalons are not specific to this example and exist for a much wider class of potentials. The ambiguity in the Borel summation of the perturbative series due to the renormalon pole is resolved by the physical condition of causality through careful consideration of the iϵ prescription. The suitably summed perturbative result coincides with the exact answer obtained through the operator formalism for scattering.

26 pages, 4 figures
лошадь, диаграмма, Фейнман

Учебное о волнах в плазме и плазменном ускорении частиц

Эх, четвертый курс, золотое время... :)

Plasma Waves in a Different Frame: a Tutorial for Plasma-based Electron Accelerators

We present an analysis of a nonlinear, relativistic longitudinal wave with sub-luminal phase velocity vp in a cold plasma. By a Lorentz transformation to a frame co-moving at velocity vp we reduce the problem to a simple second-order ordinary differential equation. Thus, the nonlinear waveform and important properties such as the maximum possible amplitude (wave-breaking limit) and the energy attainable by trapped electrons are easily obtained by exploiting the analogy with the mechanical motion of a particle in a potential well. This approach seems particularly suitable for a compact, tutorial introduction to plasma-based electron accelerators with little mathematical complexity.