Homological Perturbation Theory for Nonperturbative Integrals

Theo Johnson-Freyd*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

We use the homological perturbation lemma to produce explicit formulas computing the class in the twisted de Rham complex represented by an arbitrary polynomial. This is a non-asymptotic version of the method of Feynman diagrams. In particular, we explain that phenomena usually thought of as particular to asymptotic integrals in fact also occur exactly: integrals of the type appearing in quantum field theory can be reduced in a totally algebraic fashion to integrals over an Euler–Lagrange locus, provided this locus is understood in the scheme-theoretic sense, so that imaginary critical points and multiplicities of degenerate critical points contribute.

Original languageEnglish (US)
Pages (from-to)1605-1632
Number of pages28
JournalLetters in Mathematical Physics
Volume105
Issue number11
DOIs
StatePublished - Nov 1 2015

Keywords

  • Primary 81S40
  • Secondary 18G40

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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