Ervin Goldfain. From Multifractal Analysis to Quantum Field Theory
Natural Sciences / Physics / Quantum field theory
Submitted on: Jul 16, 2026, 12:40:04
Description: The multifractal formalism and the Euclidean Path-Integral formalism of quantum field theory (QFT) share an identical mathematical structure; both are built from the duality between a Efree energyE and a conjugate Eorder parameterE. We make this correspondence explicit, deriving the propagator, the vertex functions, the perturbative (Feynman-diagram) expansion, and the CallanE"Symanzik equation from the invariant measure properties of chaotic attractors. We identify where the correspondence is exact (the algebraic structure of Legendre duality, cumulant expansions, and RG fixed points) and where it is a physically motivated analogy requiring further justification (the identification of a specific attractor with the UV completion of a specific QFT, e.g. the Standard Model). A worked example using the Feigenbaum attractor of the logistic map illustrates the dictionary numerically. We close by outlining the conditions under which the correspondence would constitute a genuine non-perturbative definition of a QFT, rather than a suggestive isomorphism of formalisms.