arXiv:1809.00941math-ph
From Möbius inversion to renormalisation
Early discovery. Linked by one identifiable commenter. This paper is outside the main ranking; a mention is not an endorsement.
Abstract
This paper traces a straight line from classical Möbius inversion to Hopf-algebraic perturbative renormalisation. This line, which is logical but not entirely historical, consists of just a few main abstraction steps, and some intermediate steps dwelled upon for mathematical pleasure. The paper is largely expository, but contains many new perspectives on well-known results. For example, the equivalence between the Bogoliubov recursion and the Atkinson formula is exhibited as a direct generalisation of the equivalence between the Weisner--Rota recursion and the Hall--Leroux formula for Möbius inversion.
That's right! This is secretly about doing calculus on posets. You can actually generalise some notions from incidence algebras to other settings, like groupoids and categories, where you can play the same games. This is something I mostly haven't looked at yet, but I think it…
abelaerView on HNParent context