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arXiv · 1809.00941

From M\"obius inversion to renormalisation

Joachim Kock
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Abstract

This paper traces a straight line from classical M\"obius 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 M\"obius inversion.

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Joachim Kock. 2018-09-04. From M\"obius inversion to renormalisation. https://doi.org/10.4310/cntp.2020.v14.n1.a3

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