The Renormalisation Group Map

Roland Bauerschmidt, David C. Brydges, Gordon Slade

Research output: Chapter in Book/Report/Conference proceedingChapter


We introduce the renormalisation group map for the hierarchical model. The renormalisation group map has two components: a perturbative and a nonperturbative coordinate. The analysis of the renormalisation group map occupies the remainder of the book. An advantage of the hierarchical model is that the analysis can be reduced to individual blocks; this is not the case in the Euclidean setting. We explain this reduction. We discuss progressive integration; irrelevant, marginal, and relevant polynomials; and localisation. The renormalisation group map involves the notion of flow of coupling constants (uj, gj, νj), as well as the flow of an infinite-dimensional non-perturbative coordinate Kj. The flow of coupling constants is given to leading order by perturbation theory, which is derived in this chapter.

Original languageEnglish (US)
Title of host publicationLecture Notes in Mathematics
PublisherSpringer Verlag
Number of pages20
StatePublished - 2019

Publication series

NameLecture Notes in Mathematics
ISSN (Print)0075-8434
ISSN (Electronic)1617-9692


  • Localisation
  • Progressive integration
  • Renormalisation group flow equations

ASJC Scopus subject areas

  • Algebra and Number Theory


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