Appendix A: Extension to Euclidean Models

Roland Bauerschmidt, David C. Brydges, Gordon Slade

Research output: Chapter in Book/Report/Conference proceedingChapter


We give an introduction to some of the modifications needed to extend the renormalisation group method from the hierarchical to the Euclidean setting, and point out where in the literature these extensions can be found in full detail. Although the renormalisation group philosophy remains the same for the hierarchical and Euclidean models, the Euclidean setting requires significant adjustments. These include: an extended version of the perturbative coordinate, introduction of the circle product, analysis of field gradients within blocks, and more sophisticated norms involving regulators. We discuss all these items. The transfer of relevant contributions from the nonperturbative coordinate to the perturbative coordinate, in order to ensure the crucial contraction of the renormalisation group map, is now carried out via a sophisticated change of variables procedure. We also discuss this change of variables.

Original languageEnglish (US)
Title of host publicationLecture Notes in Mathematics
PublisherSpringer Verlag
Number of pages21
StatePublished - 2019

Publication series

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


  • Change of variable
  • Circle product
  • Euclidean model
  • Regulators

ASJC Scopus subject areas

  • Algebra and Number Theory


Dive into the research topics of 'Appendix A: Extension to Euclidean Models'. Together they form a unique fingerprint.

Cite this