Homological Perturbation Theory for Nonperturbative Integrals

Theo Johnson-Freyd*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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
Issue number11
StatePublished - Nov 1 2015


  • Primary 81S40
  • Secondary 18G40

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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