Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Mapping Effective Field Theory to Multifractal Geometry

Version 1 : Received: 19 May 2021 / Approved: 21 May 2021 / Online: 21 May 2021 (08:26:22 CEST)
Version 2 : Received: 24 May 2021 / Approved: 24 May 2021 / Online: 24 May 2021 (15:16:54 CEST)

How to cite: Goldfain, E. Mapping Effective Field Theory to Multifractal Geometry. Preprints 2021, 2021050502. Goldfain, E. Mapping Effective Field Theory to Multifractal Geometry. Preprints 2021, 2021050502.


Fractals and multifractals are well-known trademarks of nonlinear dynamics and classical chaos. The goal of this work is to tentatively uncover the unforeseen path from multifractals and selfsimilarity to the framework of effective field theory (EFT). An intriguing finding is that the partition function of multifractal geometry includes a signature analogous to that of gravitational interaction. Our results also suggest that multifractal geometry may offer insights into the non-renormalizable interactions presumed to develop beyond the Standard Model scale.


deterministic chaos; multifractals; effective field theory; Lyapunov exponents; Renormalization Group; selfsimilarity


Physical Sciences, Particle and Field Physics

Comments (1)

Comment 1
Received: 24 May 2021
Commenter: Ervin Goldfain
Commenter's Conflict of Interests: Author
Comment: 1) Added text on page 8 as follows:

“The so-called backward map iteration starts from the whole phase space and partitions it in a distribution of disjoint intervals, a process that is formally equivalent to coarse graining 0f the phase space [4]. It is intuitively clear that coarse graining by backward iteration mirrors the error propagation equation (18), which describes the progressive growth of separation between nearby trajectories. As a result, setting the maximal propagation error to unity, and performing the identification [4]”

2) Added text on page 13 as follows:

“Besides (39), we proceed with the following assumptions:
A1) The effective Lagrangian (34) contains individual groups of terms having the same mass dimension  . To avoid cluttering the notation, we use a single index for labeling these terms, that is,...
A2) Each operator  is the product of operators .... “  
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