Hierarchy of Analytical Methods

Abstract

In this supplementary chapter I compare a simple first-order analytic calculation done two different ways. I first compute it using the Green’s function or map method which most closely parallels the code. I then redo the calculations using the Fourier mode methods discussed in standard textbooks as well as in Sect. 8.7. These involve infinite sums which in this simple case can be carried out exactly. It should be clear that the hierarchy emerges from the extreme locality of the perturbation in accelerator physics; it is not a fundamental mathematical ordering.