Ervin Goldfain | GIRES-Global Institute for Research Education & Scholarship (original) (raw)

Drafts by Ervin Goldfain

It is nearly universally accepted that the Standard Model (SM) of particle physics, despite its r... more It is nearly universally accepted that the Standard Model (SM) of particle physics, despite its remarkable predictive power, remains an incomplete framework. Among the many longstanding puzzles confronting SM, its flavor composition, the origin of three generations, the spectrum of particle masses and charges, and the chirality of electroweak interactions continue to resist explanation. In line with our previous investigations, the goal of this exploratory work is to further bridge the gap between the universal behavior of nonlinear dynamics, on the one hand, and the flavor composition and SM chirality, on the other.

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As of today, Quantum Field Theory (QFT) and General Relativity (GR) are broadly recognized paradi... more As of today, Quantum Field Theory (QFT) and General Relativity (GR) are broadly recognized paradigms of foundational physics. There are, however, growing suspicions that both paradigms fail to hold somewhere above the Standard Model (SM) scale and in the realm of primordial cosmology. Evidence collected on multiple fronts indicates that emergence and complexity are universal features of far-from-equilibrium systems with many degrees of freedom. In line with these findings, Part 1 of this report explores the complex dynamics of evolving dimensional fluctuations beyond the SM scale. Part 2 outlines the role of complex dynamics in the nonintegrable sector of particle physics, Dark Matter condensation and the gravitational regime of the early Universe.

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A lesser-known property of Hamiltonian dynamics is that it can be formally mapped to the Riemanni... more 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 geometry of fully developed chaos, these two scales reflect the cumulative contribution of energies stored in the fractal dimensionality of spacetime. Our findings support the conjecture that both Standard and the CDM  models emerge as non-trivial attractors of the UV to infrared (IR) flow.

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Despite years of sustained research on multiple avenues, unification of Quantum Field Theory (QFT... more Despite years of sustained research on multiple avenues, unification of Quantum Field Theory (QFT) and General Relativity (GR) appears to be heading towards a dead end. There are by now dozens of review articles, blog entries, conference proceedings and reference books explaining the challenges of unification and debating the status of this presumptive failure. Yet no consensus exists on what the next steps are and on whether the whole unification effort is to be abandoned. The (modest) goal of this short review is to go over the main conceptual limitations of Quantum Gravity (QG) programs. This tutorial reflects a personal viewpoint, likely to stand at odds with the wide spectrum of opinions of those working in this field.

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The Standard Model of particle physics postulates that the (mass) ^ 2 term of the Higgs potential... more 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 that the Complex Ginzburg-Landau equation (CGLE) is a universal model of complex dynamics outside equilibrium. This brief note suggests that the tachyonic mas problem goes away upon switching from the standard Ginzburg-Landau equation to the CGLE.

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The measurement problem of Quantum Mechanics reflects the tension between the deterministic evolu... more The measurement problem of Quantum Mechanics reflects the tension between the deterministic evolution of wavefunctions and their random collapse caused by experimental observations. Here we argue that, in the Hamiltonian picture of quantum dynamics, wavefunction collapse follows from the destruction of adiabatic invariance on ultrashort time scales. We also suggest that, in the long-time limit, action quantization is a result of Arnold diffusion, a process describing the instability of nearly integrable Hamiltonian systems with more than two degrees of freedom.

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It is known that both classical and Quantum Field Theory (QFT) are built on the fundamental princ... more It is known that both classical and Quantum Field Theory (QFT) are built on the fundamental principle of stationary action. The goal of this introductory work is to analyze the breakdown of stationary action under nonadiabatic conditions. These conditions are presumed to develop far above the Standard Model scale and favor the onset of Hamiltonian chaos and fractal spacetime. The nearly universal transition to nonadiabatic behavior is illustrated using a handful of representative examples. If true, these findings are likely to have far-reaching implications for phenomena unfolding beyond the Standard Model scale and in early Universe cosmology.

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The Kibble-Zurek mechanism (KZM) describes the universal formation of topological defects in syst... more The Kibble-Zurek mechanism (KZM) describes the universal formation of topological defects in systems undergoing continuous phase transitions. KZM is traditionally applied to the study of defects in the early Universe and condensed matter phenomena. The goal of this brief report is to uncover the remarkable analogy between KZM and the flavor composition of particle physics. Our findings suggest that defect formation in particle physics and cosmology is rooted in the multifractal topology of the early Universe.

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Matter structures in cosmology include large-scale objects such as galaxies, galaxy clusters and ... more Matter structures in cosmology include large-scale objects such as galaxies, galaxy clusters and Dark Matter halos. It is widely accepted that the formation of cosmic structures in the early Universe follows from the gravitational collapse of density perturbations. Here we argue that the genesis of cosmic structures is tied to the fractal topology of spacetime near the Big Bang singularity.

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Recent research points out that the unavoidable approach to Hamiltonian chaos well above the Ferm... more Recent research points out that the unavoidable approach to Hamiltonian chaos well above the Fermi scale leads to a spacetime having continuous (fractal) dimensions. Here we analyze a toy model of inflationary Universe comprising of a Higgs-like scalar in interaction with a pair of vector bosons. The model is manifestly nonintegrable as it breaks the perturbative unitarity of scattering processes and evolves towards Hamiltonian chaos and fractal spacetime.

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The goal of this paper is to analyze the likely transition from integrability to Hamiltonian chao... more The goal of this paper is to analyze the likely transition from integrability to Hamiltonian chaos in the primordial Universe. The transition is driven by curvature fluctuations and favors the onset of a spacetime endowed with continuous dimensions.

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This is the Introduction section of the upcoming sequel to “Fractional Dynamics and the Ultraviol... more This is the Introduction section of the upcoming sequel to “Fractional Dynamics and the Ultraviolet Sector of Field Theory (Part 1)”, available at https://www.researchgate.net/publication/377778668

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Recent research points out that physics far beyond the Standard Model (SM) scale may substantiall... more Recent research points out that physics far beyond the Standard Model (SM) scale may substantially deviate from the principles of traditional field theory. The goal of this report is to briefly elaborate on the motivation for fractal spacetime and fractional dynamics in the deep ultraviolet sector of field theory.

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There are growing indications today that complex dynamics of far-from-equilibrium systems lies at... more There are growing indications today that complex dynamics of far-from-equilibrium systems lies at the root of primordial cosmology and the ultraviolet (UV) sector of particle physics. We recently pointed out that dimensional fluctuations of the UV sector can reproduce the morphology of the cosmic web. Expanding on the same line of inquiry, this provisional report explores the link between the long-range temporal correlations of critical phenomena and primordial cosmology. Excluding systematic measurement errors, our report sheds new light on the tension in the age of the Universe sparked off by the latest observations of the James Webb Space Telescope (JWST).

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Recent observations suggest that the dynamics of the primordial Universe unfolds as complex evolu... more Recent observations suggest that the dynamics of the primordial Universe unfolds as complex evolution outside thermodynamic equilibrium. Here we argue that a viable description of the primordial Universe must be built from concepts relevant to complex dynamics such as Self-Organized Criticality and Multifractal Geometry. This approach brings fresh insights into the early genesis of Dark Matter and into some outstanding challenges of standard cosmology.

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This brief note calls attention to tentative new evidence supporting the hypothesis that Dark Mat... more This brief note calls attention to tentative new evidence supporting the hypothesis that Dark Matter represents a large-scale dimensional condensate.

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Evidence from recent astrophysical experiments-including the James Webb Telescope (JWST) and Puls... more 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 note is to bring up a key challenge faced by classical gravity in far-fromequilibrium conditions. These conditions exist in the very early stages of cosmological evolution and point to a paradigm shift in our understanding of foundational physics.

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It was recently conjectured that Dark Matter consists of Cantor Dust, a relic cosmic web structur... more It was recently conjectured that Dark Matter consists of Cantor Dust, a relic cosmic web structure formed by condensation of continuous spacetime dimensions far above the Fermi scale. In this brief analysis we speculate that the Cantor Dust equations may generate the gravitational background recently reported by several international collaborations.

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Relativistic Quantum Field Theory (QFT) develops divergences caused by perturbative corrections t... more 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 particle physics. This mechanism reconciles the Higgs model of electroweak symmetry breaking with the minimal fractal topology of spacetime above the Fermi scale. Mass predictions agree reasonably well with experimental data.

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EJTP

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CSF

It is known that invariance under Lorentz transformations is a fundamental principle underlying b... more It is known that invariance under Lorentz transformations is a fundamental principle underlying both relativity and quantum field theory. It has been recently suggested that global Lorentz invariance is only an approximate symmetry of nature that may be broken for subnuclear particles participating in high-energy interactions. In particular, several research groups have argued that violation of Lorentz invariance may provide a satisfactory answer to anomalies reported in the detection of ultrahigh energy cosmic rays (UHECR) and TeV-photon spectra. Since breaking of Lorentz invariance amounts to a manifest violation of relativity, it is highly desirable to search for alternative explanations of these anomalies. Our work suggests a possible solution that complies with relativity and is consistent with the Cantorian geometry of space-time at high-energy scales.

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PSTJ

We speculate on the idea that the root cause of the recently reported diphoton excess at the Larg... more We speculate on the idea that the root cause of the recently reported diphoton excess at the Large Hadron Collider (LHC) is a nonlinear quantum optics effect. The effect is likely to arise from the strong coupling of photons to the sea of relativistic Coulomb charges carried by light quarks. Both ATLAS and CMS collaborations at the LHC have recently reported an excess of diphoton events around the invariant mass of 750 GeV, with a local significance of 3.9σ and 2.6σ, respectively [1]. The diphoton anomaly, produced in the second run of the LHC at s  13 TeV, has instantly generated an overflow of hypothetical "Beyond the Standard Model" (BSM) explanations including, but not limited to, extended Higgs sectors, heavy axions, monojet signatures of Dark Matter, hidden valleys states, dibosons, KK gravitons, goldstinos, sbinos, three body decays, dilatons, scalars from gluon fusion, photon fusion, dark pions and so on [2-3, 13]. Excluding the possibility of statistical fluctuations or unaccounted artifacts in background fitting [11-12], here we explore a speculative scenario that does not necessarily require BSM physics. The idea is that the anomaly stems from a nonlinear polarization process. The polarization is induced in the "sea" of u and d quark charges embedded in the pair of colliding protons. In particular, relativistic pp collisions transform outgoing photons into quasiparticles similar to the way polaritons arise in solid-state physics. The end result is that the system photon-relativistic "QCD matter" turns into an optical parametric amplifier. The dynamics of quark interactions in pp collisions is likely to include, besides accelerated motion, random and sustained oscillations in both color and Coulomb charges. The possibility of frequent collisions among quarks and gluons at short distances suggest that the emitted dipole radiation, referred to as pump mode, may be regarded as a quantum fluid with collective type

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CSF

Bringing closure to the host of open questions posed by the current standard model for particle p... more Bringing closure to the host of open questions posed by the current standard model for particle physics (SM) continues to be a major challenge for the theoretical physics community. Despite years of multiple research efforts, a consistent and comprehensive understanding of standard model parameters is missing. Our work suggests that critical dynamics of the renormalization group flow provides valuable insights into most of the unresolved issues surrounding SM. We report that the dynamics of the renormalization group flow and the topological approach of El Naschie's e 1 theory are viewpoints that share a common foundation. The paper concludes with a brief overview of future developments and integration efforts.

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CNSNS

The standard model for high-energy physics (SM) describes fundamental interactions between subato... more The standard model for high-energy physics (SM) describes fundamental interactions between subatomic particles 11 down to a distance scale on the order of 10 À18 m. Despite its widespread acceptance, a consistent and comprehensive 12 understanding of SM parameters is missing. Starting from a less conventional standpoint, our work suggests that the spec-13 trum of particle masses, gauge couplings and fermion mixing angles may be derived from the chaotic regime of the ren-14 ormalization group flow. In particular, we argue that the observed hierarchies of standard model parameters amount 15 to a series of scaling ratios depending on the Feigenbaum constant. Leading order predictions are shown to agree well with 16 experimental data. 17 20 21 1. Introduction 22 The generation structure of quarks and leptons stands out as one of the most intriguing puzzles of the stan-23 dard model for particle physics (SM). The conventional formulation of the SM requires 19 free input param-24 eters, among which 12 can be expressed in terms of empirical mass eigenvalues [1]. In addition, there is a set of 25 four inputs determined by the so-called Cabibbo-Kobayashi-Maskawa (CKM) matrix whose structure 26 includes three quark-mixing angles and one CP phase [18,19]. The remaining three parameters are two gauge 27 couplings (a 3 , a em) and the strong CP phase. Recent experiments in neutrino physics have confirmed the exis-28 tence of neutrino oscillations and masses and have subsequently triggered a host of challenging questions 29 [2-4]. There is a large body of proposed extensions of SM, each of them attempting to resolve some unsatis-30 factory aspects of the theory while introducing new unknowns. In contrast with the line of thought pursued by 1007-5704/$-see front matter Ó

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PSTJ

In this brief report we argue that Koide's formula arises from universal attributes of nonlinear ... more In this brief report we argue that Koide's formula arises from universal attributes of nonlinear dynamics in field theory. Feigenbaum scaling not only provides a natural paradigm for generating particle masses and coupling charges, but also a basis for understanding the family structure of fermions. A notorious shortcoming of the Standard Model (SM) for high-energy physics is its inability to explain the family structure of particle physics from first principles. Over the years, the elusive origin of SM parameters has inspired many attempts of deriving empirical formulas. These models seek to find best-fit approximation for masses of leptons and quarks but typically fail to offer compelling reasons as of why fermion replication occurs in the first place. Koide's prescription for charged lepton masses is a prime example of this endeavor. It reads [1] 2 3() 2() ee m m m m m m          (1) As it is known, SM is a theoretical framework that successfully describes non-linear interaction of leptons, quarks and gauge fields. The relevance of universal transition to chaos and of Feigenbaum scaling in particle physics has been extensively discussed in [2-4]. Recently, non-equilibrium evolution and transition to complex behavior in field theory were linked to the physics of hadronization in infrared quantum chromodynamics [5], the mechanism of mass generation and chiral symmetry breaking in SM [6]. With reference to [3, 6] and using 4 e mm     and 2 mm   

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Physica A

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Progress in Physics

Emergent physics refers to the formation and evolution of collective patterns in systems that are... more Emergent physics refers to the formation and evolution of collective patterns in systems that are nonlinear and out-of-equilibrium. This type of large-scale behavior often develops as a result of simple interactions at the component level and involves a dynamic interplay between order and randomness. On account of its universality, there are credible hints that emergence may play a leading role in the Tera-ElectronVolt (TeV) sector of particle physics. Following this path, we examine the possibility of hypothetical high-energy states that have fractional number of quanta per state and consist of arbitrary mixtures of particles and antiparticles. These states are similar to "un-particles", mass-less fields of non-integral scaling dimensions that were recently conjectured to emerge in the TeV sector of particle physics. They are also linked to "unmatter", exotic clusters of matter and antimatter introduced few years ago in the context of Neutrosophy.

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Dear Editor(s) of Physical Review Letters, This memo is in regards to the recently published cont... more Dear Editor(s) of Physical Review Letters, This memo is in regards to the recently published contribution by Ambjorn J. et al. "Planckian Birth of Quantum de Sitter Universe" PRL 100, 091304 (2008). The article claims that "causal dynamical triangulation" enables a consistent regularization of quantum gravity. A "quantum universe" emerging from a non-perturbative sum over geometries is alleged to recover "with high accuracy a four-dimensional de Sitter space-time". On closer examination, the approach is built on many objectionable premises. Specifically, 1) Quantitative models of space-time near the Planck scale, regardless of how intriguing and attractive they might be, are non-testable. One does not know if Quantum Field Theory (QFT) survives past the Cohen-Kaplan threshold of about 100 TeV, let alone what happens in close proximity to the Planck scale. The proposition that the linear size of the "quantum universe" is between 17 and 28 Planck lengths cannot be put to test. 2) Path Integral formalism and the Sum-over-Histories technique cease to be applicable in the deep TeV sector or beyond due to the likely onset of non-local interactions and chaotic dynamics of strongly coupled theories. 3) Appealing to cosmological models of space-time (such as the de Sitter model) to formulate or interpret dynamics near the Planck scale is an "ad-hoc" ansatz. There is simply no empirical evidence that supports linking the four dimensional manifold of General Relativity with physics on or below the sub-nuclear scale.

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$Research paper thumbnail of Multifractal Analysis and the Dynamics of Effective Field Theories$

PSTJ

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$Research paper thumbnail of Multifractal Geometry and Stochastic Quantization: A Brief Comparison$

PSTJ

We suggest that the multifractal geometry of the Standard Model (SM) near the electroweak scale m... more We suggest that the multifractal geometry of the Standard Model (SM) near the electroweak scale may be placed on equal footing with the stochastic quantization method. This analogy gives support to earlier attempts by Beck to derive the SM parameters using the dynamics of coupled map lattices.

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$Research paper thumbnail of Emergence of Standard Model Symmetries from Multifractal Theory$

PSTJ

Despite being supported by overwhelming evidence, the Standard Model (SM) of particle physics is ... more Despite being supported by overwhelming evidence, the Standard Model (SM) of particle physics is challenged by many foundational questions. The root cause of its gauge structure and of discrete symmetry breaking continues to be unknown. Here we show how these questions may be approached using the multifractal geometry of the SM near the electroweak scale.

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PSTJ

This brief note points out that classical Maxwell equations on fractal distributions can accommod... more This brief note points out that classical Maxwell equations on fractal distributions can accommodate fractional magnetic charges. Although these fractional objects are unobservable at energy scales significantly lower than the electroweak scale (EW M), their cumulative contribution may become relevant for charge quantization in Dirac's theory of magnetic monopoles.

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Hadronic Journal

Unitarity and locality are fundamental postulates of Quantum Field Theory (QFT). By construction,... more Unitarity and locality are fundamental postulates of Quantum Field Theory (QFT). By construction, QFT is a replica of equilibrium thermodynamics, where evolution settles down to a steady state after all transients have vanished. Events unfolding in the TeV sector of particle physics are prone to slide outside equilibrium under the combined action of new fields and un-suppressed quantum corrections. In this region, the likely occurrence of critical behavior and the approach to scale invariance blur the distinction between "locality" and "non-locality". We argue that a correct description of this far-from-equilibrium setting cannot be done outside nonlinear dynamics and complexity theory.

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PSTJ

As we have recently shown, the minimal fractal manifold (MFM) describes the underlying structure ... more As we have recently shown, the minimal fractal manifold (MFM) describes the underlying structure of spacetime near or above the electroweak scale (M EW ≈ 246 GeV). Here we uncover the connection between quantum field operators and the MFM starting from the operator product expansion of high-energy Quantum Field Theory (QFT). The approach confirms that the Standard Model of particle physics (SM) stems from a symmetry breaking mechanism that turns the spacetime continuum into a MFM. Keywords: Standard Model, broken scale invariance, infrared, minimal fractal manifold. 1. Multifractal Description of High-energy QFT QFT is plagued by several technical difficulties that challenge its consistency and predictive power in the ultraviolet (UV) region of energy scales. For example, [1]: 1) QFT operators () O x are singular at sharp points x , as they create or annihilate states with arbitrarily high energy from the vacuum, 2) Correlation functions 1 2 0 () ()... 0 O x O x are always singular, an outcome derived from the relativistic invariance and positivity of the Hilbert space, 3) Definite localization of quantum particles in space-time is impossible: Vectors having the form 4 () () 0 d x f x O x ∫ are spread across the entire Hilbert space, 4) Interacting field theories contain arbitrarily many quantum particles associated with operators acting on the vacuum, () 0 O x. In our opinion, these challenges call for a fresh perspective on the construction and interpretation of the high-energy Lagrangian, which defines a theory in a range well above the electroweak scale (246) EW M GeV ≈. The goal of this section is to elaborate on this viewpoint. We start by recalling that all perturbative QFT's with well-behaved ultraviolet (UV) behavior are thought to be described by operator product expansions (OPE's). OPE's are a standard tool in the analysis of high-energy QFT, whose applications include quantum gauge and conformally

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PSTJ

The minimal fractal manifold (MFM) defines a space-time continuum endowed with arbitrarily small ... more The minimal fractal manifold (MFM) defines a space-time continuum endowed with arbitrarily small deviations from four-dimensions 4 (, D   << 1). It was recently shown that MFM is a natural consequence of the Renormalization Group and that it brings up a series of unforeseen solutions to the challenges raised by the Standard Model. In this brief report we argue that MFM may be treated as asymptotic manifestation of Non-Commutative (NC) Field Theory near the electroweak scale. Our provisional findings may be further expanded to bridge the gap between MFM and NC Field Theory.

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CSF

One of the more striking aspects of the current Standard Model for particle physics is the replic... more One of the more striking aspects of the current Standard Model for particle physics is the replication in the total number of quarks and leptons. There are three consecutive generations of these particles and the physical significance of their grouping by mass is neither fully explained nor universally accepted. Our study suggests that the lepton mass spectrum may be recovered from the underlying chaotic dynamics of the simplest prototype for classical boson-fermion interaction, the linear r-model.

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CSF

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CSF

We develop field theoretic arguments for the unification of relativistic gravity with standard mo... more We develop field theoretic arguments for the unification of relativistic gravity with standard model interactions on El Naschie's Cantorian space-time. The work proceeds by showing the equivalence between the fundamental principle of local gauge invariance and the local scale invariance of space-time and matter fields undergoing critical behavior on high-energy scales. We focus on the transition boundary between the classical and non-classical regimes, the latter being characterized by generalized scaling laws with continuously varying exponents. Both relativistic gravity and standard model interactions emerge from the underlying geometry of Cantorian space-time near this transition boundary.

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PSTJ

As of today, the mechanism underlying the generation of mass scales in field theory remains elusi... more As of today, the mechanism underlying the generation of mass scales in field theory remains elusive. Here we show how the concept of fractal spacetime having minimal deviations from four-dimensionality (the so-called minimal fractal manifold defined through ɛ = 4-D, with ɛ << 1) can naturally account for the onset of these scales. A counterintuitive outcome of this analysis is the deep link between the minimal fractal manifold and the holographic principle.

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NOVA Science Publishers

Quantum Field Theory (QFT) lies at the foundation of the Standard Model for particle physics (SM)... more Quantum Field Theory (QFT) lies at the foundation of the Standard Model for particle physics (SM) and is built in compliance with a number of postulates called consistency conditions. The remarkable success of SM can be traced back to a unitary, local, renormalizable, gauge invariant and anomaly-free formulation of QFT. Experimental observations of recent years suggest that developing the theory beyond SM may require a careful revision of conceptual foundations of QFT. As it is known, QFT describes interaction of stable or quasi-stable fields whose evolution is deterministic and time-reversible. By contrast, behavior of strongly coupled fields or dynamics in the Terascale sector is prone to become unstable and chaotic. Non-renormalizable interactions are likely to proliferate and prevent full cancellation of ultraviolet divergences. A specific signature of this transient regime is the onset of long-range dynamic correlations in space-time, the emergence of strange attractors in phase space and transition from smooth to fractal topology. Our focus here is the impact of fractal topology on physics unfolding above the electroweak scale. Arguments are given for perturbative renormalization of field theory on fractal space-time, breaking of discrete symmetries, hierarchical generation of particle masses and couplings as well as the potential for highly unusual phases of matter that are ultra-weakly coupled to SM. A surprising implication of this approach is that classical gravity emerges as a dual description of field theory on fractal space-time.

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Vision of Oneness, Aracne Editrice, 2011

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IJTP Vol.16 No. 3/4, 2013

During the last decade, a number of important developments have surfaced concerning fractional ca... more During the last decade, a number of important developments have surfaced concerning fractional calculus and its applications in various branches of fundamental and applied science. In particular, fractional field theory (FFT) represents an active area of research in mathematical physics whose motivation stems, in part, from its ability to shed light on many of open questions surrounding Quantum Field Theory (QFT), Standard Model for particle physics (SM) and Quantum Gravity Theories (QG). We review here some recent developments of FFT that promise to recover the physics of SM in the low-energy limit and solve some of its seemingly intractable puzzles.

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Aracne Editrice, 2015

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OSA / SPIE

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SPIE

Curvature sensing is an intensity-based technique for wavefront reconstruction using two defocuse... more Curvature sensing is an intensity-based technique for wavefront reconstruction using two defocused images located on the opposite sides ofthe focal plane. It requires either one detector placed at two consecutive axial locations or a dual path with a pair of detectors from which the sensor signal is obtained. The method yields a sensitivity comparable to that of the Hartmann test in the adjustment and evaluation of ground-based optical telescopes. We introduce the analytical framework underlying the function of a curvature sensor which operates from a single defocused image. A series of twin images is computed from the propagation law of the mutual intensity along the optical axis. The polynomial decomposition of the wavefront allows retrieval of Zernike coefficients by means of the standard least-squares algorithm. The paper concludes with a review of image sampling requirements and a discussion on the signal-to-noise ratio.

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SPIE

A novel raytracing method through parabolic axial gradient index lenses is presented. The study i... more A novel raytracing method through parabolic axial gradient index lenses is presented. The study is based on developing the exact solution of the differential ray equations with initial conditions set by refraction at the first surface. The analysis offers potential benefits in reducing the computation effort and increasing the raytracing accuracy.

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SPIE

We investigate a novel method for the retrieval of an arbitrary amplitude-object which is illumin... more We investigate a novel method for the retrieval of an arbitrary amplitude-object which is illuminated from the far-field and sampled through a stratified random medium of unknown statistics. The setup includes two observation paths, a CCD-based imaging system and a multiaperture interferometer placed in a plane conjugate to the entrance pupil of the imaging system. The interferometric baselines are arranged in closed loops to make the closure phase insensitive to random refractive fluctuations. The method may be beneficial to applications such as surveillance, speckle interferometry and biomedical imaging.

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$Research paper thumbnail of Optical biopsy with long-range nondiffracting beams$

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SPIE

The paper reveals a new operating principle for a planar photonic transistor in which no electron... more The paper reveals a new operating principle for a planar photonic transistor in which no electronic components or nonlinear optical modules are used for digital switching. The author investigates the design constraints associated with the switching function, the contribution of the "noise" factors as well as the integration of the switch in a logic processor.

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PSTJ

The Standard Model for particle physics (SM) is a nonlinear field theory in which both Yang-Mills... more The Standard Model for particle physics (SM) is a nonlinear field theory in which both Yang-Mills and Higgs bosons are self-interacting objects. Their classical or quantum evolution is inevitably sensitive to the transition from order to chaos. With some noteworthy exceptions, the mainstream of theoretical particle physics has ignored the dynamical contribution of chaos in Quantum Field Theory. Here we point out that quantum corrections to the classical interaction of the Higgs with gauge bosons may lower the threshold for the onset of chaos and destabilize the vacuum in the low or intermediate TeV scale. The inability of the vacuum to survive in this energy region hints to a straightforward solution for the fine-tuning problem. It also implies that perturbative estimates on vacuum stability well above the LHC scale are likely to be invalid.

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Correlations of temperature fluctuations in the Cosmic Microwave Background are linked to the eff... more Correlations of temperature fluctuations in the Cosmic Microwave Background are linked to the effective number of neutrino flavors present in the era of recombination (N eff). The Standard Model of particle physics (SM) constrains N eff to be precisely three and all results to-date are indeed compatible with this number. However, current cosmological data consistently hint that N eff is somewhat larger than three. These findings may be the first tentative evidence for exotic matter that contains non-integer number of quanta per state, as first postulated by the author in 2006. Steven Weinberg has recently pointed out that the effective number of neutrino species derived from astrophysical measurements may be at odds with the SM, a result hinting at non-baryonic Dark Matter [1-2]. Excluding the contribution of low-sampling or systematic noise in the data, a possible solution to this apparent anomaly is to postulate the existence of Goldstone bosons emerging from breaking of a previously unknown continuous symmetry. However, a more provocative thought is to consider that all these reports are the first evidence for exotic matter composed of fractional quanta, as suggested by us in [3-7]. We believe that it is an intriguing possibility, worthy of further investigation and likely to be confirmed or falsified in the upcoming years. References: [1] http://arxiv.org/abs/1305.1971

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The diagram above shows a generic lens train for digital imaging of the human retina. I am using ... more The diagram above shows a generic lens train for digital imaging of the human retina. I am using this diagram to carry out a first-order analysis from the elementary diffraction theory of image formation. The system comprises three lenses, an aperture stop conjugate to the eye pupil and an imager. For simplicity, I assume aberration free imaging with an air-equivalent model eye whose focal length measures 17 mm (which corresponds to a normal unaccommodated eye having 1000/17 = 59 Diopters). I also assume that these are the main inputs to the optics design: 1) The required angular resolution at the imager plane is R (# of pixels/degree of the field of view). 2) The angular Field Of View (FOV) is FOV   degrees.

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PSTJ

The purpose of this brief note is to point out that, to the best of our knowledge, the first rati... more The purpose of this brief note is to point out that, to the best of our knowledge, the first rationale for modeling the Higgs scalar as mixture of electroweak bosons was disclosed in refs. [1-3]. According to this interpretation, the Higgs scalar is a topological condensate of gauge bosons on spacetime having minimal fractality.

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PSTJ

The OPERA collaboration has recently claimed discovery of superluminal propagation of neutrino be... more The OPERA collaboration has recently claimed discovery of superluminal propagation of neutrino beams. Excluding the possibility of unaccounted measurement errors, the most natural interpretation of OPERA anomaly is that, sufficiently far from the source, long-range neutrinos and photons may be regarded as components of the same field. In particular, we suggest that it is possible to construct a neutrino-photon doublet where the two components behave as dual entities. We examine conditions that enable the symmetry between neutrinos and photons to be unbroken. The benefit of this interpretation is that Lorentz invariance stays valid regardless of the relative velocity of neutrinos and their mean energy.

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Starting from the infrared limit of Yang-Mills theory, we introduce here a Higgs-free model in wh... more Starting from the infrared limit of Yang-Mills theory, we introduce here a Higgs-free model in which symmetry breaking arises from critical behavior near dimension four. Electroweak bosons develop mass near the Wilson-Fisher point of Renormalization Group flow. The family structure of Standard Model is recovered using the technique of "epsilon expansion". We also find that dimensional regularization offers a straightforward solution to the cosmological constant problem.

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viXra, 2019

Recent experiments continue to falsify the hypothesis that Dark Matter (DM) consists of quantum-l... more Recent experiments continue to falsify the hypothesis that Dark Matter (DM) consists of quantum-like particles resembling the content of the Standard Model (SM). Several arguments also exist against theories where DM arises from modifications or thermodynamic analogs of General Relativity (GR). These findings indirectly favor earlier interpretations of DM as Cantor Dust, an outcome of the minimal fractal structure of spacetime near or above the electroweak scale. Cantor Dust is consistent with the idea of Unmatter, an exotic phase containing fractional numbers of quanta per state, mixing particles with their antiparticles and carrying arbitrary non-integer spins.

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Built as a manifestly nonlinear quantum field theory (QFT), the Standard Model for particle physi... more Built as a manifestly nonlinear quantum field theory (QFT), the Standard Model for particle physics (SM) describes the low-energy interaction of gauge and Higgs bosons with quarks and leptons. Since both Yang-Mills and Higgs bosons are self-interacting fields, their behavior is inevitably sensitive to the transition from order to chaos. Here we point out that quantum corrections to the interaction of the Higgs with gauge bosons may lower the threshold for the onset of chaos and destabilize the vacuum in the low or intermediate TeV scale. The inability of the vacuum to survive in this energy region hints to a straightforward solution for the gauge hierarchy problem. It also implies that perturbative estimates on vacuum stability well above the Large Hadron Collider (LHC) scale may need to be revisited.

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viXra, 2020

We suggest here that the Higgs scalar amounts to a weakly-bounded condensate of gauge bosons. Acc... more 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.

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$Research paper thumbnail of Lorentz Symmetry from Multifractal Scaling$

viXra, 2017

We show that relativistic invariance is encoded in the multifractal structure of the Standard Mod... more We show that relativistic invariance is encoded in the multifractal structure of the Standard Model near the electroweak scale. The approximate scale invariance of this structure accounts for the flavor hierarchy and chiral symmetry breaking in the electroweak sector. Surprisingly, it also accounts for breaking of conformal symmetry in General Relativity and the emergence of a non-vanishing cosmological constant.

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Fractional-time Schrödinger equation (FTSE) describes the evolution of quantum processes endowed ... more 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 the standard index . Working in the context of the minimal fractal manifold (where , ), we confirm here that FTSE approximates the attributes of gravitational metric and provides an unforeseen generation mechanism for massive fields.

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$Research paper thumbnail of General Relativity as Multifractal Analogue of the Standard Model$

Prespacetime Journal, 2016

We have recently shown that the Standard Model of particle physics (SM) may be configured as a mu... more We have recently shown that the Standard Model of particle physics (SM) may be configured as a multifractal set, with all field components acting as primary generators of this set. The goal of this brief note is to point out that a multifractal description of General Relativity (GR) is also possible, starting from the definition of the metric tensor and relativistic interval. This finding paves the way to an unforeseen homeomorphism between the structure of SM and classical gravity.

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viXra, 2010

Both theory and experiment strongly suggest that new phenomena await discovery above the energy r... more Both theory and experiment strongly suggest that new phenomena await discovery above the energy range of the standard model for particle physics (SM). We argue that a correct description of physics in the Terascale sector needs to account for the unquenched randomness induced by short-distance fluctuations. The existence of unparticles, alleged to emerge at the next-generation colliders, is motivated by a dynamic setting that is far-of-equilibrium and able to sustain a rich spectrum of complex phenomena. Introduction Quantum Field Theory (QFT) is a framework whose methods and ideas have found successful applications in many branches of research, from particle physics and condensed matter to cosmology, statistical physics and critical phenomena [1, 2]. As a fundamental synthesis of quantum mechanics and special relativity, QFT forms the foundation for SM, a body of knowledge that describes the behavior of all known particles and their interactions except gravity. Feynman diagrams are...

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viXra, 2020

Baryon asymmetry represents the observed excess of matter over antimatter and is conjectured to f... more Baryon asymmetry represents the observed excess of matter over antimatter and is conjectured to follow from the Sakharov conditions for baryogenesis. Our brief note highlights a surprising connection between baryon asymmetry and the minimal fractality of spacetime near the Fermi scale. This connection is likely to emerge from the non-equilibrium regime of dimensional fluctuations in the early Universe.

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Prespacetime Journal, 2012

We give a concise but incomplete list of reasons why Quantum Gravity and Higher-Dimensional field... more We give a concise but incomplete list of reasons why Quantum Gravity and Higher-Dimensional field theories are likely to point in the wrong direction. For the sake of clarity and due to the vast volume of research on these topics, no references are included. The interested reader can search for key words relevant to the context using Google Scholar or similar internet engines.

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viXra, 2012

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Prespacetime Journal, 2013

Recent years have hinted that the concept of fractal spacetime may play a role in both the “would... more Recent years have hinted that the concept of fractal spacetime may play a role in both the “would-be” physics beyond the Standard Model and the large-scale structure of the Universe. Here we explore a scenario where classical spacetime equipped with minimal fractality appears to provide a natural solution for two major challenges of relativistic cosmology, the cosmological constant and coincidence problems.

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viXra, 2020

Self-organized criticality (SOC) reflects the ability of many complex dynamical systems to self-s... more Self-organized criticality (SOC) reflects the ability of many complex dynamical systems to self-sustain critical behavior outside equilibrium. Here we provide analytic evidence that quantum field propagators and the probability distribution of SOC share a common foundation. In particular, we find that the formal structure of quantum propagators replicates the finite scaling ansatz (FSS) of SOC, which is a generic paradigm for the emergence of complexity in Nature.

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viXra, 2010

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Bulletin of the American Physical Society, 2008

Emergent physics refers to the formation and evolution of collective patterns in systems that are... more Emergent physics refers to the formation and evolution of collective patterns in systems that are nonlinear and out-of-equilibrium. This type of large-scale behavior often develops as a result of simple interactions at the component level and involves a dynamic interplay between order and randomness. On account of its universality, there are credible hints that emergence may play a leading role in the Tera-ElectronVolt (TeV) sector of particle physics. Following this path, we examine the possibility of hypothetical highenergy states that have fractional number of quanta per state and consist of arbitrary mixtures of particles and antiparticles. These states are similar to “un-particles”, massless fields of non-integral scaling dimensions that were recently conjectured to emerge in the TeV sector of particle physics. They are also linked to “unmatter”, exotic clusters of matter and antimatter introduced few years ago in the context of Neutrosophy.

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Prespacetime Journal, 2011

This brief report suggests a straightforward solution for the hierarchy problem of the Standard M... more This brief report suggests a straightforward solution for the hierarchy problem of the Standard Model using dimensional regularization of quantum field theory (QFT). Our viewpoint breaks away from traditional approaches to the hierarchy problem based on supersymmetry (SUSY), Technicolor, extra-dimensions, anthropic arguments, fine-tuning or gauge unification near the Planck scale.

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Prespacetime Journal, 2020

It is well known that both Newtonian gravity and General Relativity can be built starting from th... more It is well known that both Newtonian gravity and General Relativity can be built starting from the classical Poisson equation in 3-dimensional space. Here we speculate that, at least in principle, the concept of 3-dimensional space equipped with minimal fractality enables a qualitative explanation of both rotation curves of disk galaxies and cosmological expansion. Our approach bridges the gap between particle and gravitational interpretations of Dark Matter and suggests a unified picture of the Dark Sector. It offers a basis for explaining away Modified Newtonian Gravity (MOND) and its theoretical ramifications.

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As of today, the nature of Dark Matter (DM) remains controversial. Broadly speaking, there are tw... more As of today, the nature of Dark Matter (DM) remains controversial. Broadly speaking, there are two major schools of thought on the topic. While the first school considers DM to be an extrapolation of particle physics, the second one asserts that DM is a signature of gravitational phenomena. The basic tenet of the second school of thought is that DM can be explained away either through revisions of General Relativity (GR), through its inherent nonlinearity or by deploying non-traditional interpretations of GR. The goal of this brief note is to point out that DM and gravitational physics may no longer be mutually exclusive, but complementary manifestations of the same reality. Elaborating from the minimal fractality of spacetime above the Fermi scale along with its quaternion formulation we suggest that DM can replicate the contribution of gravitational nonlinearities on galactic scales.

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viXra, 2008

Unitarity and locality are fundamental postulates of Quantum Field Theory (QFT). By construction,... more Unitarity and locality are fundamental postulates of Quantum Field Theory (QFT). By construction, QFT is a replica of equilibrium thermodynamics, where evolution settles down to a steady state after all transients have vanished. Events unfolding in the TeV sector of particle physics are prone to slide outside equilibrium under the combined action of new fields and un-suppressed quantum corrections. In this region, the likely occurrence of critical behavior and the approach to scale invariance blur the distinction between "locality" and 2non-locality". We argue that a correct description of this far-from-equilibrium setting cannot be done outside nonlinear dynamics and complexity theory.

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viXra, 2010

Understanding the origin of certain symmetry breaking scenarios in high-energy physics remains an... more Understanding the origin of certain symmetry breaking scenarios in high-energy physics remains an open challenge. Here we argue that, at least in some cases, symmetry violation is an effect of non-equilibrium dynamics that is likely to develop somewhere above the energy scale of electroweak interaction. We also find that, imposing Poincare symmetry in non-equilibrium field theory, leads to fractalization of space-time continuum via period-doubling transition to chaos.

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Prespacetime Journal, 2020

Matching current observations on non-baryonic Dark Matter (DM), Cantor Dust was recently conjectu... more Matching current observations on non-baryonic Dark Matter (DM), Cantor Dust was recently conjectured to emerge as large-scale topological structure formed in the early stages of cosmological evolution. The mechanism underlying the formation of Cantor Dust hinges on dimensional condensation of spacetime endowed with minimal fractality. It is known that anyons are quasiparticles exhibiting anomalous statistics and fractional charges in 2+1 spacetime. This brief report is a preliminary exploration of the intriguing analogy between anyons and the Cantor Dust picture of DM.

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