Nonperturbative Contribution to Φ+U: Proof of Theorem 8.2.5

Roland Bauerschmidt, David C. Brydges, Gordon Slade

Research output: Chapter in Book/Report/Conference proceedingChapter


We prove the main estimates on the nonperturbative contribution to the flow of coupling constants, i.e., to the flow of the perturbative coordinate of the renormalisation group map. This proves one of the two main theorems from the previous chapter. The proof makes use of an “extended norm” which is defined in this chapter. The main work in the proof rests on the proof of various norm estimates for polynomials in the field. A more comprehensive set of estimates on polynomials, needed for the next chapter, is also presented here.

Original languageEnglish (US)
Title of host publicationLecture Notes in Mathematics
PublisherSpringer Verlag
Number of pages11
StatePublished - 2019

Publication series

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


  • Flow of coupling constants
  • Polynomial norm estimates
  • Renormalisation group flow

ASJC Scopus subject areas

  • Algebra and Number Theory


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