Ervin Goldfain

Ronin Institute · Physics Department

As of today, the reason for the unique composition of the Standard Model (SM) gauge group remains elusive. Taking complex-scalar field theory as baseline model, we argue here that the SM group unfolds sequentially from bifurcations driven by the Renormalization scale. Numerical estimates are found to be reasonably consistent with experimental data.

This is a brief rundown on some of my research projects that are currently in the planning stage. My goal is to further explore the conjecture that complex dynamics of nonlinear systems lies at the heart of foundational physics. The anticipated completion timeframe for these contributions is the end of 2024.

The mechanism of Arnold diffusion (AD) describes the dynamic instability of nearly-integrable Hamiltonian systems. Here we argue that AD leads to action quantization for classical systems having an infinite number of degrees of freedom. Planck's constant emerges as long-time value of the action differential applied to large ensembles of oscillators...

This is a selection of my papers on Complex Dynamics and Effective Field Theory

As long-cherished postulate of theoretical physics, Hamilton's principle (HP) defines the basis of classical mechanics and field theory. We argue here that HP is overturned in physical settings where sensitivity to initial conditions cannot be ignored. We find that the approach to chaos of nearly-integrable Hamiltonian systems sheds new light on se...

Evidence from recent astrophysical experiments-including the James Webb Telescope (JWST) and Pulsar Timing Arrays (PTA)-reveal potential inconsistencies with standard Big-Bang cosmology [1-4]. Several competing explanations of these (and similar) anomalies have been suggested, but a conclusive resolution is yet to be seen. The object of this brief...

This report expands on the preprint "Dimensional Regularization as Mass Generating Mechanism", posted at the following sites: https://doi.org/10.32388/DW6ZZS , https://www.researchgate.net/publication/370670747

The purpose of this document is to disseminate reviewers' comments and author's replies on the preprint posted at [1] and [2].

The purpose of this document is to disseminate reviewers' comments and author's replies on the preprint posted at [1] and [2].

The purpose of this document is to disseminate reviewers' comments and author's replies on the preprint posted at [1] and [2]. The second version of this preprint is currently in progress.

Fractals and multifractals are self-similar structures endowed with _continuous dimensions_. This tutorial traces the origins of fractal spacetime to the universal features of Hamiltonian chaos, conjectured to develop far above the Fermi scale (\(v=246\)GeV). A representative signature of Hamiltonian chaos is the _fragmentation ofphase-space_ into...

Relativistic Quantum Field Theory (QFT) develops divergences caused by perturbative corrections to Feynman diagrams. Dimensional Regularization (DR) is a technique that isolates divergences using analytic continuation to non-integer dimensions. In this introductory tutorial we argue that DR provides an alternative mechanism for mass generation in p...

This is Part 2 of the brief tutorial "Hamiltonian Chaos and the Fractal Topology of Spacetime" posted at https://www.researchgate.net/publication/369584882.

Fractals and multifractals are self-similar structures endowed with continuous dimensions. This tutorial traces the origins of fractal spacetime to the universal features of Hamiltonian chaos, conjectured to develop far above the Fermi scale. A representative signature of Hamiltonian chaos is the fragmentation of phase-space into islands of stabili...

Dimensional Reduction (DR) conjectures that the number of spacetime dimensions monotonically drops with the boost in the energy scale. According to DR, the expectation is that ordinary space progressively unfolds from being one or two-dimensional near the Big-Bang singularity. This work argues that DR a) can explain some of the observed anomalies c...

The Standard Model of particle physics postulates that the (mass) ^ 2 term of the Higgs potential is negative. This choice is considered unnatural and leads to the tachyonic mass problem. It is known that the formulation of the Higgs mechanism relies on the standard Ginzburg-Landau equation describing equilibrium phase transitions. It is also known...

Complex Ginzburg-Landau equation (CGLE) is a universal model of nonequilibrium dynamical systems. Focusing on the primordial stages of cosmological evolution, this work points out that the connection between CGLE and the Navier-Stokes (NS) equation bridges the gap between fluid flows and the mathematics of General Relativity (GR).

The time dependent Ginzburg Landau equation (TGLE) is a prototype model of non-equilibrium statistical physics and critical phenomena. This brief report points out that, applying TGLE to the chaotic dynamics of interacting fields hints to unexpected solutions to the challenges confronting high-energy theory.

The Stuart-Landau (SL) equation describes the universal behavior of nonlinear oscillators near a Hopf bifurcation. Focusing on the ultraviolet sector of field theory, the goal of this brief report is to explore the relationship between the SL equation and the spin-statistics theorem of Quantum Field Theory (QFT).

We argue here that the onset of classical chaos above the Fermi scale underlies the construction of Effective Field Theory (EFT). According to this view, particle physics and gravitational dynamics are low-energy manifestations of chaotic behavior and multifractal geometry.

We argue here that the high-energy behavior of fundamental interactions can be interpreted as manifestation of Kolmogorov (-K) entropy. The conventional classification of fields based on Poincaré symmetry appears to be rooted in the chaotic regime of nonlinear dynamics far above the Standard Model scale.

It is known that large-scale dynamical systems can sustain a rich variety of collective phenomena. This brief note argues that the cosmology of the early Universe can be viewed as critical behavior in continuous dimensions. We find that the self-similar properties of the metric near the Big Bang singularity are comparable to the effects produced by...

The Kolmogorov (K-) entropy quantifies the continuous transition from deterministic evolution to fully developed chaos. We argue here that, in the early Universe, multi-body Newtonian gravity emerges from the properties of the K-entropy. This finding also suggests that, far above the Fermi scale, gravitational physics and field theory are coexistin...

Despite its technical appeal, the main drawback of the gauge-gravity duality is that it works with a negative cosmological constant, in manifest contradiction with observations. We point out here that a 2D spacetime endowed with minimal fractality acquires a positive cosmological constant upon combining the gauge-gravity duality with the dimensiona...

The Higgs mechanism of electroweak symmetry breaking (EWSB) has several conceptual challenges that are currently unresolved. We recently put forward an alternative embodiment of EWSB based on sequential field bifurcations driven by the Renormalization scale. This brief report points out that the bifurcation scenario can evade three shortcomings of...

Fuzzy Dark Matter (FDM) models are of class of theories where Dark Matter (DM) is interpreted as condensate of ultralight scalar or pseudoscalar particles. Few years back we conjectured that a spacetime endowed with minimal fractality enables a natural association of FDM to Cantor Dust, an early Universe phase induced by topological condensation of...

This brief note points out that, if early cosmology drives gravitational dynamics out of equilibrium, a straightforward random walk model of orbital motion can explain away the basis of Modified Newtonian Dynamics (MOND).

The gravitational dynamics of many-body systems is a replica of Hamiltonian chaos, whose phase-space description requires the tools of multifractal analysis. Multifractals are collections of self-similar sets and their distribution of continuous dimensions follows a singularity spectrum. Building on the multifractal characterization of Black Holes...

Over the years, naturalness has been a key principle for guiding theory development beyond the Standard Model (BSM) and for solving the cosmological constant (CC) problem. The discovery of the Higgs boson and the exclusion of several BSM scenarios at the Large Hadron Collider (LHC) has set off an ongoing debate on the conceptual limitations of the...

Emergent gravity builds upon the formal connection between classical Thermodynamics and the field equations of General Relativity. Drawing from the thermodynamic interpretation of multifractals, we speculate here that gravitational dynamics follows from the multifractal geometry of spacetime far above the Fermi scale. Our brief report suggests that...

Fractional statistics (FS) is a generalization of the spin-statistics theorem and mixes bosons and fermions in a non-trivial way. Mixing is controlled by a continuous parameter q and the ordinary statistics is recovered in the limit q = 1. We have argued some time ago that the onset of FS occurs in a spacetime endowed with minimal fractality, whose...

The motivation for the continuous dimensionality of spacetime near the Fermi scale stems from two premises, namely, 1) dimensional regularization of perturbative quantum field theory (QFT), 2) the existence of non-trivial fixed points of Renormalization Group equations. Here we discuss a third reason, rooted in the behavior of non-equilibrium phase...

We have recently conjectured that the Standard Model gauge group unfolds under successive bifurcations of the Higgs potential. This brief report points out that the maximal fixed-point solution of the bifurcation diagram coincides with a top-antitop quark condensate.

A lesser-known property of Hamiltonian dynamics is that it can be formally mapped to the Riemannian geometry of classical gravitation. Taking advantage of this property, we explore here the possibility that the onset of Hamiltonian chaos in the ultraviolet (UV) sector of field theory generates the cosmological and Fermi scales. In line with the geo...

We recently pointed out that the numerical value of the vacuum energy parameter derived via the Friedmann model may be reasonably approximated within the framework of Stochastic Cosmology. This brief note shows that the Hubble constant prediction of Stochastic Cosmology also falls in line with observational data.

In this brief pointer we bring attention to the growing evidence supporting the multifractal geometry of effective field theory and the large-scale structure of the Universe.

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...

As paradigm of complex behavior, multifractals describe the underlying geometry of self-similar objects or processes. Building on the connection between entropy and multifractals, we show here that the generalized dimension of geodesic trajectories in General Relativity coincides with the four-dimensionality of classical spacetime.

The evolution of integrable classical systems leads to conserved quantities and vanishing Poisson brackets. In contrast, such invariants do not exist in the dynamics of non-integrable systems, which include (but are not limited to) deterministic models with long-term chaotic behavior. The object of this review is to briefly survey the mathematical...

It is known that the divergence of vacuum energy density (VED) in Quantum Field Theory lies at the core of the cosmological constant (CC) problem. Our brief note suggests that, at least in principle, modeling the quantum vacuum as an ensemble of fractional oscillators may regulate the ultraviolet behavior of the VED and evade the CC problem.

We suggest here that the Higgs scalar amounts to a weakly-bounded condensate of gauge bosons. According to this interpretation, the Higgs mass may be approximated from the sum of vector boson masses on spacetime endowed with minimal fractality.

Self-organized criticality (SOC) is a universal mechanism for self-sustained critical behavior in large-scale systems evolving outside equilibrium. Our report explores a tentative link between SOC and Lagrangian field theory, with the long-term goal of bridging the gap between complex dynamics and the non-perturbative behavior of quantum fields.

In condensed matter theory, Hamiltonian time crystals (HTC) are time-dependent solutions of the equation of motion that develop in a minimum energy configuration. A subset of HTC's includes periodic trajectories that spontaneously break time-translation invariance and occur at a local minimum of the free energy. Recent studies suggest that HTC's ma...

Fractional-time Schrödinger equation (FTSE) describes the evolution of quantum processes endowed with memory effects. FTSE manifestly breaks all consistency requirements of quantum field theory (unitarity, locality and compliance with the clustering theorem), unless the order of fractional differentiation and integration falls close to one. Working...

The purpose of this note is to draw attention to several open issues related to Penrose's singularity theorem of 1965.

Complex Ginzburg-Landau equation (CGLE) is a paradigm for the onset of chaotic patterns and turbulence in nonlinear dynamics of extended systems. Here we point out that the underlying connection between CGLE and the Navier-Stokes (NS) equation bridges the gap between fluid flows, on the one hand, and the mathematics of General Relativity (GR) and c...

Our earlier work has tentatively shown that the hierarchy of fermion masses and mixing angles follows from the universal behavior of nonlinear dynamics. In this brief sequel we survey a similar scenario in which the Cabibbo angle arises from the nonlinear dynamics of charged-current interactions.

This work is a top-level summary of several contributions published in the last three decades. It makes the case that complex dynamics of nonlinear systems lies at the heart of foundational physics.

The goal of this report is to tentatively show that the hierarchy of fermion masses and mixing angles follows from the universal behavior of nonlinear dynamics. Our work breaks away from attempts of explaining the Standard Model (SM) based upon heavy fields, postulated objects in complex spaces, non-commutative or motivic geometry, Quantum Gravity...

The purpose of this brief Addendum is to elaborate on a couple of relationships introduced in Physica A 165: 399-419 (1990).

The Standard Model (SM) fails to account for either the triplication of fermion families or chiral symmetry breaking in the electroweak sector. Here we show that both phenomena arise from the approach to chaos of quantum theory near the Fermi scale.

The power spectrum of the cosmic microwave background (CMB) quantifies the distribution of relic radiation left over from the early Universe. As of today, CMB data acquired by Planck and WMAP satellites exhibit certain anomalies that challenge the standard model of cosmology (ΛCDM). The goal of this brief report is to sketch up an intriguing connec...

In this brief addendum we clarify the interpretation of the Gaussian Random Walk model of spacetime introduced in PSTJ, July 2020, 11 (4), pp. 314-317.

We have shown over recent years that the dynamics of quantum fields is likely to slide outside equilibrium above the Fermi scale of electroweak interactions. In proximity to this scale, spacetime dimensionality flows with the probing energy and leads to the concept of minimal fractal manifold (MFM). It is known that modeling the physics on fractal...

Iterated maps are deterministic models of dynamical systems in discrete time. A key feature of these models is the concept of invariant density associated with the asymptotic onset of stationarity. Drawing from the minimal fractality of spacetime near the Fermi scale, we show here that invariant density enables a step-by-step derivation of Quantum...

We argue that the fundamental symmetries of effective field theory can be traced to the onset of self-similarity. In particular, the scale-free structure of fractal geometry lies at the heart of invariance principles in classical and quantum field theory.

Last decade has seen mounting evidence that complex dynamics can shed new light on many open questions of contemporary theoretical physics. Starting from this vantage point, our goal here is to show that Lie groups and the gauge structure of the Standard Model follow from the universal framework of self-organized criticality (SOC). In particular, w...

We explore the idea that Minkowski spacetime and the principle of locality reflect the asymptotic properties of self-organized criticality (SOC). Both properties arise from demanding that the scaling behavior of space and time coordinates follows the power-law distribution of Gaussian random walks.

We have shown over recent years that the dynamics of quantum fields is likely to slide outside equilibrium above the Fermi scale of electroweak interactions. In proximity to this scale, spacetime dimensionality flows with the probing energy and leads to the concept of minimal fractal manifold (MFM). The goal of this brief report is to combine the M...

Iterations of continuous maps are the simplest models of generic dynamical systems. In particular, circle maps display several key properties of complex dynamics, such as phase-locking and the quasi-periodicity route to chaos. Our work points out that Planck's constant may be derived from the scaling behavior of circle maps in the asymptotic limit.

We point out that Newton's constant may be interpreted as adiabatic invariant of metric oscillations in the far-field approximation of General Relativity.

We explore the idea that three universal constants of theoretical physics reflect the asymptotic approach to self-similarity and adiabatic invariance of weakly coupled oscillators.

Iterations of continuous maps are the simplest models of generic dynamical systems. In particular, circle maps display several key properties of complex dynamics, such as phase-locking and the quasi-periodicity route to chaos. Our work points out that Planck's constant may be derived from the scaling behavior of circle maps in the asymptotic limit.

We have shown over recent years that the dynamics of quantum fields is likely to slide outside equilibrium above the Fermi scale of electroweak interactions. In proximity to this scale, spacetime dimensionality flows with the probing energy and leads to the concept of minimal fractal manifold (MFM). The goal of this brief report is to combine the M...

Last decade has seen mounting evidence that complex dynamics can shed new light on many open questions of contemporary theoretical physics. Starting from this vantage point, our goal here is to show that Lie groups and the gauge structure of the Standard Model follow from the universal framework of self-organized criticality (SOC). In particular, w...

We explore the idea that Minkowski spacetime and the principle of locality reflect the asymptotic properties of self-organized criticality (SOC). Both properties arise from demanding that the scaling behavior of space and time coordinates follows the power-law distribution of Gaussian random walks.

Self-organized criticality (SOC) is a universal mechanism for self-sustained critical behavior in large-scale systems evolving outside equilibrium. The trademark signature of SOC is twofold: a) it occurs in complex ensembles of multiple interacting components and b) it is characterized by power-law distribution of "avalanche" sizes. This brief repo...

Self-organized criticality (SOC) is a universal mechanism for self-sustained critical behavior in large-scale systems evolving outside equilibrium. Our report explores a tentative link between SOC and Lagrangian field theory, with the long-term goal of bridging the gap between complex dynamics and the non-perturbative behavior of quantum fields.