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REVIEW 4 major objections 3 minor 88 references

Approximate Minimal SU(5), Several Fundamental Scales, Fluctuating Lattice

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Pith's one-line read The paper claims that eight or nine fundamental energy scales, from the Planck mass down to hadronic-string and domain-wall scales, fall on one straight line as different moments of a single wildly fluctuating lattice.

desk verdict A self-aware speculative fit of nine scales to a log-normal lattice line; the new g-2 section is an in-sample consistency check rather than a prediction. read the letter →

arxiv 2505.06716 v1 pith:TVGJSRIR submitted 2025-05-10 hep-ph hep-lat

Holger Bech Nielsen This is my paper · ORCID
classification hep-phhep-lat
keywords fluctuatinglatticelog-normaldistributionenergyscalehierarchyapproximateSU(5)GrandUnifiedTheoriesPlanckanomalousmagneticmomentontological
topics Dark Matter
open problems Dark Matter
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper attempts to show that the huge gaps between fundamental energy scales are not separate coincidences but one statistical fact. It assumes the world lives on a real, ontological lattice whose link size fluctuates wildly from region to region with a log-normal, or Galton, distribution. A scale depending on the $n$th power of the link length then has typical energy $\left(\langle a^n\rangle^{1/n}\right)^{-1}=a_0^{-1}\exp(-n\sigma/2)$, so logarithms of scales fall on a straight line against the integer $n$ with only two free parameters. The fit covers the Planck scale, an approximate non-supersymmetric SU(5) unification near $5\times10^{13}$ GeV, inflation and seesaw scales, the fermion-tip scale of $10^4$ GeV, a 28 GeV monopole candidate, the hadronic string scale, and dark-matter domain walls. The same fitted scales are then used to reproduce the small electron and muon anomalous-magnetic-moment deviations from the Standard Model.

What carries the argument

The machine is the Galton, i.e. log-normal, distribution of the lattice link size, written $P(\ln a)\,d\ln a=\frac{1}{\sqrt{2\pi}\sigma}\exp\left(-\frac{(\ln a-\ln a_0)^2}{2\sigma}\right)d\ln a$, together with the moment identity $\langle a^n\rangle^{1/n}=a_0\exp(n\sigma/2)$. Because the $n$th-root moment separates into an $n$-dependent exponential, one broad spread $\sigma$ converts different powers $n$ into exponentially different energy scales. The integer $n$ for each scale is read off from the mass dimension of the relevant Lagrangian coefficient, with the sign chosen according to whether the term is kinetic or non-kinetic; the paper's table uses the shifted integer $E=n+4$ as the abscissa, and the fitted line is $10^4\,\mathrm{GeV}\times250^{-n}$.

What would settle it

Compute, from the lattice action itself, the power of $a$ that appears in the effective gravitational constant rather than taking it from the restricted-second-derivative argument of Section 2; if a first-principles calculation yields a moment other than $\langle a^{-6}\rangle^{1/6}$, the Planck scale leaves the fitted line. Alternatively, measure any new scale with a cleanly assigned $n$ from its Lagrangian dimension—the line predicts a $\langle a^4\rangle^{1/4}$ scale near $10^4\,\mathrm{GeV}\times250^{-4}\approx2.5$ keV—and check whether it sits on the line.

Watch

Extended reading notes

Core claim

The central claim is that every fundamental energy scale is an order-of-magnitude determination of the same fluctuating lattice. For a link size $a$ with log-normal distribution, the identity $\langle a^n\rangle^{1/n}=a_0\exp(n\sigma/2)$ makes the inverse energy scale $a_0^{-1}\exp(-n\sigma/2)$ linear in $n$, so a plot of log energy versus the power $n$ is a straight line. Each scale is assigned an integer $n$ from the dimension of the Lagrangian term that defines it: $n=-6$ for the Planck scale via $1/G\propto\langle a^{-6}\rangle$, $n=-4$ for the approximate non-supersymmetric SU(5) scale via the gauge kinetic term, $n=0$ for the fermion-tip extrapolation of $10^4$ GeV, $n=1$ for the monopole-dimuon scale near 28 GeV, $n=2$ for the hadronic string scale, and $n=3$ for the dark-matter domain-wall scale. With $a_0^{-1}\approx10^4$ GeV and $\exp(\sigma/2)\approx250$, eight to nine scale entries agree with their fitted values, while supersymmetric SU(5) unification at $10^{16}$ GeV falls off the line and is therefore disfavoured by the scheme.

Load-bearing premise

The load-bearing premise is that each named energy scale is controlled by exactly one integer power of the local link size, with the power read off from the Lagrangian dimension and all dimensionless prefactors of order unity—if any real scale mixes moments or carries a large prefactor, the straight line becomes a choice, and the paper itself flags the sixth-power Planck derivation as dangerous.

Editorial extensions

If this is right

  • If the straight line is correct, the hierarchy between the unification scale and the Planck scale needs no finely tuned desert of intermediate new physics: fluctuations of one lattice produce the exponential separations.
  • The same two parameters place the approximate non-supersymmetric SU(5) meeting near $5\times10^{13}$ GeV while putting supersymmetric SU(5) unification at $10^{16}$ GeV off the line, so the scheme disfavours low-energy supersymmetry.
  • The hadronic string scale and the dark-matter domain-wall tension become reflections of the same link-size distribution rather than purely QCD-determined quantities, which the author notes is an intriguing consequence.
  • The g-2 analysis predicts a negative electron anomaly, selecting the caesium-determined fine-structure constant over the rubidium one, and a positive muon anomaly of the right order, although the muon sign is not predicted because the string scale of 0.16 GeV lies close to the muon mass.
  • Lattice cut-off effects would set in near the fermion-tip scale of $10^4$ GeV, far below the Planck scale, making the first nonlocal lattice effects potentially visible at much lower energies than quantum gravity is usually expected to appear.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the line is taken literally, it predicts a tower of further scales at integer spacings of about 250 in energy: for example a scale controlled by $\langle a^4\rangle^{1/4}$ would sit near $10^4\,\mathrm{GeV}\times250^{-4}\approx2.5$ keV, a range already probed by astrophysical spectral searches; the paper does not draw this connection.
  • The g-2 success depends on assigning the overall prefactor to the monopole scale via $\langle a/m\rangle^2$ while putting the string scale inside the logarithm via $\langle(a/m)^2\rangle$; a derivation that explains why the two factors decorrelate would convert a two-parameter fit into a sharper prediction and would test the claimed electron sign.
  • Because a log-normal distribution is the generic outcome of many multiplicative fluctuations, the width $\sigma$ might not be a free parameter in a more complete dynamical model; if the lattice itself settles the width by self-consistency, the scheme could predict the ratio 250 rather than fit it.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 3 minor

Summary. The paper proposes that a truly existing, strongly fluctuating lattice with a log-normal distribution of link sizes can generate a wide hierarchy of physical energy scales. Its central claim is Eq. (3): for a log-normal distribution of link size a, the inverse nth-root moment <a^n>^{-1/n} equals a0^{-1} exp(-n sigma/2), so log E versus n is a straight line with two parameters, a0 and sigma. The paper assigns an integer power n to each of about nine energy scales—Planck, approximate SU(5) unification, inflation, see-saw, scalar, fermion-tip, monopole, hadronic string, and domain wall—and reports that the measured values fall on this line. It then uses the line's parameters, specifically the 'string' and 'monopole' scales, in a simple cutoff integral to estimate the electron and muon anomalous magnetic moment deviations from the Standard Model, claiming good agreement. The paper is transparent about several weak points, including an explicitly 'dangerous' step in the Planck-power derivation and an admitted freedom in choosing which scale enters the g-2 formula.

Significance. If the linear relation were derived from first principles and if the nine scales were independently measured, the result would be striking: a two-parameter description of scales spanning some 25 orders of magnitude. The paper also has virtues: the arithmetic of Eq. (3) and of the table is simple and reproducible, and the author explicitly flags the weakest derivation step and the adjustable choices in the g-2 section, which is scientifically honest. However, as presented, the central claim is not yet a prediction: the n assignments are largely post hoc, several input scales are model-dependent or invented, and the g-2 check is in-sample with admitted freedom of choice. The paper should not be published as a substantive result without a first-principles derivation of the powers and an out-of-sample test.

major comments (4)
  1. [Section 3.3, Eq. (85)] The straight line is a two-parameter fit, not a prediction. The power n for each scale is assigned after the scale is chosen, and the table itself marks several assignments as uncertain: the inflation entries carry '?' for their powers, the see-saw scale is labeled 'modeldependent' and is admitted in Section 3.2 to be uncertain by several orders of magnitude, and the 'scalars' scale is labeled 'invented by me'. With n as a free choice per scale, the agreement in the third column is in-sample and merely determines a0^{-1} and exp(sigma/2).
  2. [Section 2, Eqs. (57)-(60i)] The Planck power n = -6 is the steepest anchor of the fit and largely sets the slope, but its derivation is explicitly flagged by the author as 'dangerous' immediately after Eq. (60i), and the full calculation is only alluded to from the companion paper [1]. Since a one-unit change in this power destroys the fit (as the stress-test note also observes), the central line is not robust without a reliable derivation of this exponent.
  3. [Section 4.4 and 4.6] The g-2 agreement is not an independent confirmation. In Section 4.4 the author explicitly allows 'adjust which of the two energy scales, the string scale or the monopole scale, to use at the two different places in the very simple formula', which is a 2-by-2 choice, or 8 possibilities if the fine-structure constant choice is included. The two scales are themselves outputs of the same line fit, and the fitted values are extracted from the very data being explained. The author also admits that the sign of the muon deviation is not predicted. Thus the claimed success is a fit with adjustable choices, not a prediction.
  4. [Section 5 and Table 3.3] The claim of a 'remarkable coincidence' relies on about nine scales, but the author's own conclusion states that only four of the nine are 'not so ill defined' (Planck, approximate SU(5), fermion tip, and hadronic string), with the monopole as a possible fifth if one accepts the speculative dimuon interpretation. The remaining entries—scalars, domain walls, inflation-derived scales, and see-saw—are either invented, model-dependent, or poorly determined. With two fitted parameters and only four or five solid points, the statistical weight of the claimed straight line is far weaker than the paper suggests.
minor comments (3)
  1. [Abstract and throughout] There are numerous typographical errors, including 'straght line' in the abstract, 'Chanse' in the conclusion, and inconsistent units in the table (e.g., 'Gev' vs. 'GeV'). A careful proofreading pass is needed.
  2. [Section 4, Eqs. (94)-(108)] The notation in the representative-integral calculation is difficult to follow, with several garbled fractions and unclear replacements (e.g., the arrow notation in Eq. (94f) and the treatment of the integration measure). Clarifying the steps would help the reader verify the arithmetic.
  3. [References] Several references have corrupted DOI strings, such as [7] with 'zero.alt3' placeholders, and reference [78] is the present paper itself; the reference list needs to be cleaned and completed.

Circularity Check

4 steps flagged · score 7.0 of 10

Central 'predictions' reduce to fitted or selected inputs: the fermion tip is the line's intercept by definition, the Planck power is self-flagged and imported from the author's companion paper, and the g-2 success is an in-sample choice among eight alternatives.

  1. self definitional [Section 2, Eq. (28); Table 3.3, 'Fermion tip' row; Eq. (86)]
    "we should take M_tip = 1/a0. (28)"

    The fermion-tip scale is defined to be the inverse of the log-normal location parameter a0, i.e. the n=0 intercept of Eq. (3). The fitted-value formula (86) is written as 10^4 GeV × 250^{-n}, so the point at n=0 automatically reproduces 10^4 GeV. Listing 'Fermion tip' in the table as a scale whose measured and fitted values agree is therefore a tautology: the tip is not a test of the straight line but one of the two parameters that defines it.

  2. ansatz smuggled in via citation [Section 2, Eqs. (57)-(61), and text after Eq. (60i)]
    "Reduced Planck constant 1/√κ ≈ 6√<a^{-6}> (61) ... but this last step sounded dangerous. ... This calculations of the relevant powers deserves some further development, and a slightly different calculation is found in [1], and is actually alluded to in the table."

    The n=-6 Planck anchor controls the steepness of the whole line: with a0^-1=10^4 GeV and exp(σ/2)=250 it sets E(Planck)=2.4×10^18 GeV, while n=-5 would require exp(σ/2)≈750 and move the n=-4 unification prediction off by two orders of magnitude. The derivation of this crucial exponent is explicitly called dangerous and the complete version is deferred to the author's companion paper [1], which is a self-citation rather than an independent, machine-checked or externally reproduced calculation. The key power is therefore imported as an ansatz from the authors' own prior work.

2 more flagged steps
  1. fitted input called prediction [Section 4.4, paragraph after Eq. (125); Section 4.6]
    "Now we allow ourselves to adjust which of the two energy scales, the 'string scale' ∼ 0.16 GeV or the 'monopole scale' 40 GeV or 27 GeV, to use at the two different places in the very simple formula (137)... we fitted the two anomalous magnetic moment deviation by selecting one possibility among 2 × 2 = 4 possibilities. If ... Cs or the Rb measurement, we would have chosen among 8 possibilities..."

    The advertised 'surprisingly good' g-2 numbers are not a parameter-free prediction. After seeing the data the author selects which fitted scale enters the prefactor, which enters the logarithm, and which fine-structure determination (Cs vs Rb) to trust, i.e. one of 2×2×2=8 configurations. Section 4.6 then explicitly fits the two continuous parameters 'monopole scale' and 'string' to the two measured g-2 deviations and compares them with the line-fit values; with two data points and two fitted parameters, plus the discrete selection, the agreement is an in-sample consistency check rather than a prediction. The paper itself concedes 'it is not so great to fit with two parameters'.

  2. other [Section 3.2 and Figure 2 caption]
    "Concerning these cosmological scales about inflation, I do not feel safe as to what should be our power B, but believe we got it right with B=-5 for the V^{1/4} and B=-4 for the H. ... For the first a^{-4} and for the second a^{-5} was chosen, and then it fits well."

    For the inflation entries the power n is not derived before the fit; the author states he does not feel safe and 'chose' B=-5 and B=-4, and only then 'it fits well'. This makes those two of the nine 'scales' line up by construction: the n assignment is adjusted to achieve the fit. The table marks the inflation powers with '?', confirming that these entries are not independent confirmations of the straight line.

full rationale

The mathematical core Eq. (3) is a standard log-normal moment identity and is not circular. A two-parameter fit of a set of independently chosen energy scales to a straight line is also a legitimate exercise; the hadronic string, domain wall, unification and Planck points could in principle have failed to align. However, several load-bearing steps reduce the claimed successes to their inputs. (1) The fermion-tip scale is defined as 1/a0, so the table row at n=0 is the intercept by construction rather than a data point. (2) The Planck power n=-6, which sets the slope of the line, is derived via a step the author calls 'dangerous' and is completed only by citation to the same author's companion paper [1]; the power is therefore imported rather than independently demonstrated. (3) The g-2 deviations, highlighted in the abstract as a success, are obtained after choosing among 8 discrete options (which scale in the prefactor, which in the logarithm, Cs vs Rb) and, in Section 4.6, by fitting two continuous parameters to the two measured deviations. This is an in-sample fit, not an out-of-sample prediction. (4) The inflation scales are assigned powers n post hoc so that they fit. These issues do not make every entry in the table circular — the hadronic string scale, for example, comes from an independent Regge-slope measurement — but they mean the central claim is substantially weaker than 'nine scales predicted by two parameters'. The core straight-line fit retains some independent content, so the paper is not entirely circular; it is partially circular at the level of the specific 'predictions' that the abstract emphasizes.

Assumptions & free parameters 6 free parameters · 6 assumptions · 5 invented entities

The claimed straight line rests on two fitted parameters, hand-assigned powers n for each scale, and the assumption that all prefactors are order unity. The g-2 check adds further choices about which average to use and which energy scale enters each factor. None of these ingredients is derived from a first-principles lattice action.

free parameters (6)
  • a0 (lattice link scale), quoted as 1/a0 = fermion tip scale = a0^{-1} ~ 10^4 GeV in the main fit; 1.7e3 GeV in the Section 1.2 pedagogy
    Intercept of the straight-line log-energy versus n plot; set by the fermion tip extrapolation rather than derived from a lattice action.
  • sigma (width of log-normal link distribution) = exp(sigma/2) ~ 250 in the main fit
    Slope of the line; extracted from pairwise ratios of scales, with the paper quoting 214, 270, 61, and 63 from different scale pairs.
  • power assignments n for the nine scales = Planck -6, unification -4, inflation H -4, inflaton potential -5, see-saw -3, scalars -2, fermion tip 0, monopole 1…
    Chosen per scale from dimensional analysis of Lagrangian terms; a change in any n moves the point horizontally and can spoil or restore the line fit.
  • monopole energy scale used in g-2 fit = 55.0 +/- 13% GeV from the backward fit; table value 40 GeV, dimuon hint 27 GeV
    Extracted from the electron and muon deviations in Section 4.6, not predicted before the comparison.
  • string energy scale used in g-2 fit = 0.0790 GeV from the backward fit; table value 0.128 GeV with the 2.18 factor
    Extracted from the muon deviation after fixing the monopole scale; the paper calls it a success despite a factor 1.6 difference.
  • cutoff constant c in sinh(c)/c = 2.18
    Hand-chosen so that sinh(c)/c equals 2; it affects the logarithm in the g-2 estimate but is presented only as an order-unity choice.
assumptions (6)
  • domain assumption The link size a has a Galton (log-normal) distribution with a large width sigma.
    Eq. (2); no dynamical derivation is given, only a reference to Gibrat's multiplicative-fluctuation argument.
  • domain assumption All lattice coupling parameters and prefactors are of order unity.
    Section 1.2, around Eqs. (9)-(13); if prefactors are not order one, the scale relations acquire extra factors that are not controlled.
  • domain assumption Each physical scale is dominated by one power average <a^n>^(1/n) with integer n read off from the dimension of a Lagrangian coefficient.
    Used for all table entries, e.g. Planck from <a^-6>, unification from <a^-4>, string from <a^2>; the paper admits the Planck derivation is 'dangerous'.
  • domain assumption The approximate SU(5) unification scale 5.3e13 GeV and the three-family factor of 3 are taken from the author's previous model [2].
    Section 1, Eq. (53); the factor 3 is explained by three layers of lattices, one per family, an assumption not independently tested.
  • domain assumption The numerical values of the empirical scales (10^11 GeV see-saw, 10^14 GeV inflation H, 7 MeV domain wall, 27 GeV dimuon) are accepted from model-dependent sources.
    Section 3.2; the paper itself says the see-saw scale is uncertain by orders of magnitude and the domain wall tension estimates range from 4 to 12 MeV.
  • domain assumption The fermion tip scale of 10^4 GeV follows from a parabolic extrapolation of Standard Model fermion masses to fermion number zero.
    Section 2, Eqs. (29)-(30); the parabola is fitted to the mass spectrum, not derived from the lattice model.
invented entities (5)
  • Ontological fluctuating lattice (a truly existing lattice)
    purpose: Underlying discrete space-time whose fluctuating link sizes generate all energy scales as different power averages.
    Postulated as the basis of the model; no independent observable except through the claimed scale relations.
  • Three layers of lattices, one per fermion family
    purpose: Multiplies the quantum correction to the SU(5) coupling running by 3 to match observed deviations from exact unification.
    Introduced in Section 1 to fix a factor-3 discrepancy; no independent evidence is provided.
  • Scalar scale with many scalar bosons and vacuum expectation values near it
    purpose: Explains the small hierarchy problem and provides weak symmetry breakings that generate fermion mass ratios.
    The paper explicitly calls it 'only my phantasy' and 'invented by me' in the table status and conclusion.
  • Standard Model monopoles of mass around 27 GeV, or a hadron-like bound state of such monopoles
    purpose: Identifies the monopole scale on the straight line and suggests a dimuon resonance as experimental evidence.
    The CMS and ALEPH dimuon excesses cited are not established resonances, and the monopole interpretation is speculative.
  • Dark matter domain walls (pearls) from the Froggatt-Nielsen model
    purpose: Provides the domain-wall scale of about 7 MeV used as one of the nine plotted scales.
    The dark matter model is from prior work by the same group, and the 3.5 keV line it invokes is disputed in the cited literature.

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Cite this review

Pith. "Pith review of Approximate Minimal SU(5), Several Fundamental Scales, Fluctuating Lattice." pith.science (2026). https://pith.science/paper/TVGJSRIR

@misc{pith2026250506716,
  author       = {Pith},
  title        = {Pith review of: Approximate Minimal SU(5), Several Fundamental Scales, Fluctuating Lattice},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TVGJSRIR}},
  note         = {Machine review of arXiv:2505.06716}
}
read the original abstract

Having shortly reviewed our idea of the grand unified SU(5) being only exact in a classical limit, in a truly existing lattice, an ontological lattice, we go over to putting a series of different physical energy scales such the approximate unification scale for the SU(5)(without any SUSY), the Planck scale, and e.g. the scale of see-saw neutrino masses into a certain plot showing the energy scales on a straight line. This straight line of this plot supposed to result from such an ontological lattice, that fluctuates in link size a and lattice density in a very strong way according to a log normal distribution. The point is that different energy scales result from the link size of the lattice to different powers, like the averages a to the n th , where the power n depends on the type of scale considered. Since the n th root of the average of the n th power of the link size in the fluctuating lattice is very strongly dependent on the power n, because of very huge fluctuations, the different types of physical energy scales can get very different. With a Galton i.e. log normal distribution of the link size the various energy scales have their logarithms fall into a nice straight line versus the power of the link size, on which they depend. Our model gives a surprisingly good number for the small deviations of the experimental electron-and muon-anomalous magnetic moment from the pure Standard Model value.

Figures

Figures reproduced from arXiv: 2505.06716 by the authors.

Figure 1
Figure 1. Because the distribtuion of log links after size has a maximum at the fermion tip point, we suggest that also the density of activ fermions (=fermions with lower mass than the scale , at which you ask for the density of links) should behave this way, meaning with a parabola behavior with maximum at the point (=the fermion tip point). If we take it that there are 45 or 44 chiral fermions per family the number of fami… view at source ↗
Figure 2
Figure 2. Here we see how the energy scales ,along the abscissa,the logarithms of them, (for easiness of cal￾culation we used basis 10 logartihm). They all fit within expected accuracy except as it is put here the “inflation scale” for which is it not so obviuos what to take for = 4 + = 4 + “the power for a relevant for averaging”. In the table we decided that there were two scales involved with inflation, the Hubble-Lemaitre… view at source ↗
Figure 3
Figure 3. Similar figure as figure 2 but only with reduced Planck scale for the Planck scale, and written with just dots to let us enjoy how ell it fits the straight line. The cosmological entries looks worst and susy grand unification was left out. The see-saw- scale is simply the mass order of magnitude for the see-saw neutrinos which in the see-saw model cause the neutrino oscillations of the observed Standard model neutri… view at source ↗

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Reference graph

Works this paper leans on

88 extracted references · 63 canonical work pages

  1. [1]

    Remarkable Scale Relation, Approxi mate SU(5), Fluctuating Lattice

    Holger B. Nielsen, “ Remarkable Scale Relation, Approxi mate SU(5), Fluctuating Lattice”, published in Universe (Rigel Li): universe-3501361, submi tted 13. february 2025, accepted

    2025

  2. [2]

    Approximate SU(5), Fine Structure Constants

    Nielsen, H.B. Approximate SU(5), Fine structure consta nts. , arXiv:2403.14034

    work page Pith review arXiv

  3. [3]

    On Absolute Units, I: Ch oices

    See e.g. Wilczek, Frank (2005). "On Absolute Units, I: Ch oices". Physics Today. 58 (10). American Institute of Physics: 12–13. Bibcode:2005PhT... .58j..12W . doi:10.1063/1.2138392. Misner, Charles W .; Thorne, Kip S.; Wheeler, John A. (1973). Gravitation. New Y ork. ISBN 0-7167-0334-3. OCLC 585119

    doi:10.1063/1.2138392 2005

  4. [4]

    The fundamental scales of structures from first principles

    Funkhouser, S. “The fundamental scales of structures fr om first principles.” 2008 , arXiv:0804.2443

    work page Pith review arXiv 2008

  5. [5]

    Can We Push the Fundamental Planck Scale A bove 10 19 GeV?

    Stojkovic, D. “Can We Push the Fundamental Planck Scale A bove 10 19 GeV?” Available online: htttps://cds.cern.ch (accessed on)

  6. [6]

    Wilson fermion doubling phenomenon on irregular lattice: the similarity and difference with the case of regular lattice

    Vergeles, S.N. “Wilson fermion doubling phenomenon on i rregular lattice: The similarity and difference with the case of regular lattice.” arXiv 2015 , arXiv:1502.03349v2

    work page Pith review arXiv 2015

  7. [7]

    Lattice quantum hadrodynamic s

    Brockmann, R.; Frank, J. “Lattice quantum hadrodynamic s” Phys. Rev. Lett. 1992, 68, 1830. https://doi.org/1/zero.alt3.11/zero.alt33/PhysRevLett.68.183/zero.alt3

    1992

  8. [8]

    Advanced Lattice QCD Desy 98-017 August 200 6

    Lüscher, M. “Advanced Lattice QCD Desy 98-017 August 200 6” (lectures)

Show all 88 references
  1. [9]

    Fluctuating lattice Boltzman n method for the diffusion equation

    Wagner, A.J.; Strand, K. “Fluctuating lattice Boltzman n method for the diffusion equation.” Phys. Rev. E 2016, 94, 033302. https://doi.org/1/zero.alt3.11/zero.alt33/PhysRevE.95./zero.alt3699/zero.alt33

    2016

  2. [10]

    On the spontaneous origin of Newtons con stat

    Minkowski, P. “ On the spontaneous origin of Newtons con stat” Phys. Lett. B 1977, 67, 421. Mohapatra, R.N.; Senjanovic, G. Phys. Rev. Lett. 1980, 44, 912

    1977

  3. [11]

    Naturally Massless Higgs Doublets in Supersymmetric SU(5)

    Masiero, A.; Nanopoulos, A.; Tamvakis, K.; Y anagida, T . “Naturally Massless Higgs Doublets in Supersymmetric SU(5)”. Phys. Lett. B 1982, 115, 380–384. https://doi.org/1/zero.alt3.1/zero.alt316//zero.alt337/zero.alt3-2693(82)9/zero.alt3522-6

    1982

  4. [12]

    Unity of all elementary-parti cle forces

    Howard, G.; Sheldon, G. “Unity of all elementary-parti cle forces.” Phys. Rev. Lett. 1974, 32,

    1974

  5. [13]

    On the Gibrat Distribution

    Kalecki, M. “On the Gibrat Distribution.” Econometrica 1945, 13, 161–170

    1945

  6. [14]

    A model of income distribtu ion

    Pestieau, P.; Possen, U.M. “A model of income distribtu ion.” Eur. Econ. Rev. 1982, 17, 279–294. 32 Several scales Holger Bech Nielsen

    1982

  7. [15]

    14: Lognorm al Distributions

    Johnson, N.L.; Kotz, S.; Balakrishnan, N. “14: Lognorm al Distributions”, Continuous uni- variate distributions. In Wiley Series in Probability and Mathematical Statistics: A pplied Probability and Statistics, 2nd ed.; John Wiley & Sons: New Y ork, NY, USA, 1994; Volume 1, ISB...

    1994

  8. [16]

    Phas e Transition in Gauge Theories and Multiple Point Model

    Laperashvili, L.V .; Nielsen, H.B.; Ryzhikh, D.A. Phas e Transition in Gauge Theories and Multiple Point Model. arXiv 2001, arXiv:hep-th/0109023

    2001 arXiv

  9. [17]

    [/u1D446/u1D448(5)] 3 SUSY unification

    Laperashvili, L.; Ryzhikh, D. “ [/u1D446/u1D448(5)] 3 SUSY unification.” arXiv 2001, arXiv:hep- th/0112142

    2001

  10. [18]

    Introduction: Gut and Anti-Gut ; Oxford University Press: Oxford, UK, 2009; pp

    Volovik, G.E. Introduction: Gut and Anti-Gut ; Oxford University Press: Oxford, UK, 2009; pp. 1–8. https://doi.org/1/zero.alt3.1/zero.alt393/acprof:oso/978/zero.alt3199564842./zero.alt3/zero.alt33./zero.alt3/zero.alt3/zero.alt31

    2009

  11. [19]

    Critical Couplings And Three Generations in a Random-Dynamics Inspired Model

    Picek, I. “Critical Couplings And Three Generations in a Random-Dynamics Inspired Model.” Fizika B 1992, 1, 99–110

    1992

  12. [20]

    What comes beyond the standard models

    Bennett, D.L.; Laperashvili, L.V .; Nielsen, H.B. Fine structure Constants at the Planck scale from Multiple Point Prinicple. In Proceedings of the Tenth W orkshop “What comes beyond the standard models”, Bled, Slovenia, 17–27 July 2007; Volu me 8

    2007

  13. [21]

    Bennett, D.; Nielsen, H.B.; Picek, I. Phys. Lett. B 1988, 208, 275

    1988

  14. [22]

    Random Dynamics and relations between t he number of fermion generations and the fine structure constants

    Nielsen, H.B. “Random Dynamics and relations between t he number of fermion generations and the fine structure constants.” Acta Phys. Pol. Ser. B 1989, 20, 427

    1989

  15. [23]

    Gauge Glass

    Nielsen, H.B.; Brene, N. “ Gauge Glass”. In Proceedings of the XVIII International Symposium on the Theory of Elementary Particles, Ahrenshoop, 1985 (In stitut fur Hochenergi-physik, Akad. der Wissenschaften der DDR, Berlin-Zeuthen, 1985); D .L. Bennett, N. Brene, L. Mizrachi

    1985

  16. [24]

    Nielsen, H.B. Phys. Lett. B 1986, 178, 179

    1986

  17. [25]

    Predictions for Nonabeli an Fine Structure Constants from Mul- ticriticality

    Bennett, D.L.; Nielsen, H.B. Predictions for Nonabeli an Fine Structure Constants from Mul- ticriticality. arXiv 1993, arXiv:hep-ph/9311321v1

    1993 arXiv

  18. [26]

    Gauge Couplings Calcula ted from Multiple Point Criticality Yield /u1D6FC−1 = 137 ± 9: At Last, the Elusive Case of U(1)

    Bennett, D.L.; Nielsen, H.B. “Gauge Couplings Calcula ted from Multiple Point Criticality Yield /u1D6FC−1 = 137 ± 9: At Last, the Elusive Case of U(1).” arXiv 1996, arXiv:hep-ph/9607278

    1996 arXiv

  19. [27]

    Baryogenesis via lepton n umber violation in Anti-GUT model

    Nielsen, H.B.; Takanishi, Y . Baryogenesis via lepton n umber violation in Anti-GUT model. arXiv 2001, arXiv:hep-ph/0101307

    2001 arXiv

  20. [28]

    [/u1D446/u1D448(5)] 3 SUSY unification

    Laperashvili, L.V .; Das, C. “ [/u1D446/u1D448(5)] 3 SUSY unification.” arXiv 2001, arXiv:hep-th/0112142

    2001 arXiv

  21. [29]

    Deconfinement phase transitions in e xternal fields

    Cea, P.; Cosmai, L. Deconfinement phase transitions in e xternal fields. In Proceedings of the XXIIIrd International Symposium on Lattice Field Theory, T rinity College, Dublin, Ireland, 25–30 July 2005. 33 Several scales Holger Bech Nielsen

    2005

  22. [30]

    Pha se transition couplings in U(1) and SU(N) regularized gauge theories

    Laperashvili, L.V .; Ryzhikh, D.A.; Nielsen, H.B. “Pha se transition couplings in U(1) and SU(N) regularized gauge theories.” Int. J. Mod. Phys. A 2001, 16, 3989–4009. https://doi.org/10.1142/S0217751X01005067

    2001 doi

  23. [31]

    Laperashvili, L.V .; Nielsen, H.B.; Ryzhikh, D.A. Int. J. Mod. Phys. A 2001, 16, 3989. Laperashvili, L.V .; Nielsen, H.B.; Ryzhikh, D.A. Yad. Fiz. 2002, 65

    2001

  24. [32]

    Flipped SU(5), see-saw scale physics and degenerate vacua

    Das, C.R.; Froggatt, C.D.; Laperashvili, L.V .; Nielse n, H.B. “Flipped SU(5), see-saw scale physics and degenerate vacua.” arXiv 2005, arXiv:hep-ph/0507182

    2005 arXiv

  25. [33]

    Random Dynamics and Relations Between th e Number of Fermion Generations and the Fine Structure Constants

    Nielsen, H.B. Random Dynamics and Relations Between th e Number of Fermion Generations and the Fine Structure Constants

  26. [34]

    What comes Beyand the Standard Models

    Nielsen, H.B.; Kleppe, A.; et al. Bled Workshop July 201 9, “What comes Beyand the Standard Models”. Available online: http://bsm.fmf.uni-lj.si/bled2/zero.alt319bsm/talks/HolgerTransparencesconfusion2.pdf (accessed on)

  27. [35]

    The Confusion Mechanism and the Heterotic String

    Bennett, D.L.; Nielsen, H.B.; Brene, N.; Mizrachi, L. “ The Confusion Mechanism and the Heterotic String.” In Proceedings of the 20th Internationa l Symposium on the Theory of Elementary Particles, January 1987

    1987

  28. [36]

    Seeking a Game in which the s tandard model Group shall Win

    Nielsen, H.B.; Bennett, D. “Seeking a Game in which the s tandard model Group shall Win.” Bled Work. Phys. 2011, 12, 149

    2011

  29. [37]

    Small Representations Explaining, Why standard model group?

    Nielsen, H.B. “Small Representations Explaining, Why standard model group?” PoS CORFU 2015, 2014, 045

    2015

  30. [38]

    Dimension Four Wins the Same Game as the Sta ndard Model Group

    Nielsen, H. “Dimension Four Wins the Same Game as the Sta ndard Model Group.” Phys. Rev. D 2013, 88, 096001

    2013

  31. [39]

    The Dawning of Gauge Theory; Princeton University Press: Princeton, NJ, USA, 1997

    O’Raifeartaigh, L. The Dawning of Gauge Theory; Princeton University Press: Princeton, NJ, USA, 1997

    1997

  32. [40]

    Complex Action Support from Coincidenc es of Couplings

    Nielsen, H.B. “Complex Action Support from Coincidenc es of Couplings.” arXiv 2011, arXiv:1103.3812v2

    2011 arXiv

  33. [42]

    Foerster, D.; Nielsen, H.B.; Ninomiya, M. Phys. Lett. B 1980, 94, 135

    1980

  34. [43]

    Ultracold Quantum Gases and Lattice Syst ems: Quantum Simulation of Lattice Gauge Theories

    Wiese, U.-J. “Ultracold Quantum Gases and Lattice Syst ems: Quantum Simulation of Lattice Gauge Theories.” arXiv 2013, arXiv:1305.1602v1

    2013 arXiv

  35. [44]

    Seeking Inspi ration from the Standard Model in Order to Go Beyond It

    Nielsen, H.B.; Rugh, S.E.; Surlykke, C. “Seeking Inspi ration from the Standard Model in Order to Go Beyond It.” arXiv 1994 , arXiv:hep-th/9407012. 34 Several scales Holger Bech Nielsen

    1994 arXiv

  36. [45]

    Froggatt, C.D.; Nielsen, H.B.; Takanishi, Y . Nucl. Phys. B 2002, 631, 285. Nielsen, H.B.; Takanishi, Y .Phys. Lett. B 2002, 543, 249

    2002

  37. [46]

    Masses and mixing angle s and going beyond the Standard Model

    Nielsen, H.B.; Froggatt, C.D. “Masses and mixing angle s and going beyond the Standard Model.” arXiv 1999, arXiv:hep-ph/9905445. Froggatt, C.D.; Nielsen, H.B. Hierarchy of quark masses, Ca bibbo angles and CP violation. Nucl. Phys. B 1979, 147, 277. Nielsen, H.B.; Takanishi, Y...

    1999 arXiv

  38. [47]

    Fermion masses, critical behavior and universality.arXiv 2023, arXiv:2302.11580

    Feruglio, F. Fermion masses, critical behavior and universality.arXiv 2023, arXiv:2302.11580

    2023 arXiv

  39. [48]

    School and Workshops on Elementary Particle Physics and Gravity

    Nielsen*, H.B.; Froggatt, C.D. Volume 376—Corfu Summer Institute 2019 “School and Workshops on Elementary Particle Physics and Gravity” (CORFU2019)—Connecting Insights in Fundamental Physics: Standard Model and Beyond. Several degenerate vacua and a model for DarkMatter in the...

    2019

  40. [49]

    Formulation of Complex Actio n Theory

    Nagao, K.; Nielsen, H.B. “Formulation of Complex Actio n Theory.” arXiv 2012, arXiv:1104.3381v5

    2012 arXiv

  41. [50]

    1) Nielsen, H.B.; Ninomiya, M. Int. J. Mod. Phys. A 2006, 21, 5151

    2006

  42. [51]

    Minimal SU(5) theory on the edge: The importance of being effective

    Senjanovic, G.; Zantedeschi, M. “Minimal SU(5) theory on the edge: The importance of being effective.” arXiv 2024, arXiv:2402.19224v1. 35 Several scales Holger Bech Nielsen

    2024 arXiv

  43. [52]

    Who is Afraid of the Past

    Bennett, D.L.; Froggatt, C.D.; Nielsen, H.B. the proceed ings of Wendisch-Rietz 1994 -Theory of elementary particles- , p.394-412; the proceedi ngs of Adriatic Meeting on Particle Physics: Perspectives in Particle Physics ’94, p.255-279. Talk given by D. L. Bennett, “Who is Af...

    1994 arXiv

  44. [53]

    The proceedings of Bled 2006— What Comes Beyond the Standard Models-, pp

    Nielsen, H.B.; Ninomiya, M. The proceedings of Bled 2006— What Comes Beyond the Standard Models-, pp. 87–124, arXiv:hep-ph/0612250

    2006 arXiv

  45. [54]

    arXiv:0802.2991 [physics.g en-ph]; Int

    Nielsen, H.B.; Ninomiya, M. arXiv:0802.2991 [physics.g en-ph]; Int. J. Mod. Phys. A 23 (2008) 919; Prog. Theor. Phys. 116 (2007) 851

    2008 arXiv

  46. [55]

    the proceedings of Bled 2007— What Comes Beyond the Standard Models, pp

    Nielsen, H.B.; Ninomiya, M. the proceedings of Bled 2007— What Comes Beyond the Standard Models, pp. 144–185

    2007

  47. [56]

    arXiv:0910.0359 [hep-ph]; t he proceedings of Bled 2010— What Comes Beyond the Standard Models, pp

    Nielsen, H.B.; Ninomiya, M. arXiv:0910.0359 [hep-ph]; t he proceedings of Bled 2010— What Comes Beyond the Standard Models, pp. 138–157

    2010 arXiv

  48. [57]

    arXiv:1006.2455 [physic.gen-ph]

    Nielsen, H.B. arXiv:1006.2455 [physic.gen-ph]

    arXiv

  49. [58]

    arXiv:hep-th/0701018

    Nielsen, H.B.; Ninomiya, M. arXiv:hep-th/0701018

    arXiv

  50. [59]

    arXiv:0911.3859 [gr-qc]

    Nielsen, H.B. arXiv:0911.3859 [gr-qc]

    arXiv

  51. [60]

    The proceedings of Bled 2010—What Comes Beyond the Standard Models, pp

    Nielsen, H.B.; Borstnik, M.S.M.; Nagao, K.; Moultaka, G . The proceedings of Bled 2010—What Comes Beyond the Standard Models, pp. 211–216

    2010

  52. [61]

    Nagao, K.; Nielsen, H.B. Prog. Theor. Phys. 2011, 125, 633

    2011

  53. [62]

    Nonabelian Monopoles

    Auzzi, R.; Bolognesi, S.; Evslin, J.; Konishi, K.; Mura yama, H. “Nonabelian Monopoles”. arXiv 2004, arXiv:hep-th/0405070v3

    2004 arXiv

  54. [63]

    Grand Unified Theories: SU (5), SO(10) and sup ersymmetric SU (5)

    Thoren, J. Grand Unified Theories: SU (5), SO(10) and sup ersymmetric SU (5). Bachelor’s Thesis, Lund University, Lund, Sweden, 2012

    2012

  55. [64]

    Phase transitions in gauge and spin-latt ice systems

    Migdal, A.A. “Phase transitions in gauge and spin-latt ice systems”. Zh. Eksp. Teor. Fiz. 1975, 69, 1457–1465

    1975

  56. [65]

    Neutrino Mass and Mixing in the Seesaw Playgr ound

    King, S.F. Neutrino Mass and Mixing in the Seesaw Playgr ound. Available on- line:www.sciencedirect.com (accessed on). Nucl. Phys. B 2016, 908, 456–466. Available online: www.elsevier.com/locate/nuclphysb (accessed on)

    2016

  57. [66]

    Physics of Neutrino Mass

    Mohapatra, R.N. “ Physics of Neutrino Mass.” SLAC Summe r Institute on Particle Physics (SSI04), Aug. 2-13, 2004

    2004

  58. [67]

    A neutrino mass matrix with see saw mechanism and two-loop mass splitting

    Grimus, W .; Lavoura, L. “ A neutrino mass matrix with see saw mechanism and two-loop mass splitting.” arXiv 2000, arXiv:hep-ph/0007011v1

    2000 arXiv

  59. [68]

    A lower bound on the right-han ded neutrino mass from leptogenesis

    Davidson, S.; Ibarra, A. “A lower bound on the right-han ded neutrino mass from leptogenesis.” arXiv 2002, arXiv:hep-ph/0202239v2

    2002 arXiv

  60. [69]

    Cosmological Inflation

    Enquist, K. “Cosmological Inflation.” arXiv 2012, arXiv:1201.6164v1

    2012 arXiv

  61. [70]

    An Introduction to Cosmological Inflation

    Liddle, A. An Introduction to Cosmological Inflation. arXiv 1999, arXiv:astro-ph/9901124v1

    1999 arXiv

  62. [71]

    Measuring the Energy Scale of Inflation with Large Scale Structures

    Bellomo, N.; Bartolo, N.; Jimenez, R.; Matarrese, S.; V erde, L. “Measuring the Energy Scale of Inflation with Large Scale Structures.” arXiv 2018, arXiv:1809.07113v2

    2018 arXiv

  63. [72]

    Froggatt, C.D.; Nielsen, H.B. Nucl. Phys. B 1979, 147, 277–298

    1979

  64. [73]

    Quark model and the factorization of the Veneziano amplitude

    Nambu, Y . (1970). "Quark model and the factorization of the Veneziano amplitude." In R. Chand (ed.), Symmetries and Quark Models: Proceedings of the International Conference held at Wayne State University, Detroit, Michigan, June 18–20, 1 969 (pp. 269–277). Singapore: World S...

    1970

  65. [74]

    Search for resonances in the ma ss spectrum of muon pairs produced in association with b quark jets in proton-proton collision s at √/u1D460= 8 and 13 TeV

    The CMS Collaboration. “Search for resonances in the ma ss spectrum of muon pairs produced in association with b quark jets in proton-proton collision s at √/u1D460= 8 and 13 TeV .”arXiv 2018, arXiv:1808.01890v2

    2018 arXiv

  66. [75]

    Observation of an excess at 30 GeV in the opposite sign di-muon spectra of /u1D44Dß /u1D44F/u1D44F+ /u1D44Bevents recorded by the ALEPH experiment at LEP

    Heister, A. “Observation of an excess at 30 GeV in the opposite sign di-muon spectra of /u1D44Dß /u1D44F/u1D44F+ /u1D44Bevents recorded by the ALEPH experiment at LEP”. arXiv 2016, arXiv:1610.06536v1

    2016 arXiv

  67. [76]

    Dynamical s tability of local gauge symmetry Creation of light from chaos

    Foerster, D.; Nielsen, H.B.; Ninomiya, M. “ Dynamical s tability of local gauge symmetry Creation of light from chaos.” Phys. Lett. B 1980, 94, 135–140

    1980

  68. [77]

    Field theories without fundamental gaug e symmetries

    Nielsen, H.B. Field theories without fundamental gaug e symmetries. Phi- los. Trans. R. Soc. Lond. Ser. A Math. Phys. Sci. 1983, 310, 261–272. https://doi.org/1/zero.alt3.1/zero.alt398/rsta.1983./zero.alt3/zero.alt388,

    1983

  69. [78]

    Time translatio nal symmetry

    Lehto, M.; Nielsen, H.B.; Ninomiya, M. Time translatio nal symmetry. Phys. Lett. B 1989, 219, 87–91. 36 Several scales Holger Bech Nielsen

    1989

  70. [79]

    Solà , J. J. Phys. Conf. Ser. 2013, 453, 012015

    2013

  71. [80]

    Domain Walls and Hubble C onstant Tension

    Froggatt, C.D.; Nielsen, H.B. Domain Walls and Hubble C onstant Tension. arXiv 2024, arXiv:2406.07740. https://doi.org/1/zero.alt3.4855/zero.alt3/arXiv.24/zero.alt36./zero.alt3774/zero.alt3

    2024 arXiv

  72. [81]

    String Invention, Viable 3-3-1 Model, Da rk Matter Black Holes

    Nielsen, H.B. String Invention, Viable 3-3-1 Model, Da rk Matter Black Holes. arXiv 2024, arXiv 2409.13776

    2024 arXiv

  73. [82]

    Universal regge slope /u1D6FC′ from the QCD gluon propagator

    H.B. Nielsen, M. Ninomiy, “Universal regge slope /u1D6FC′ from the QCD gluon propagator” Physics Letters B Volume 92, Issues 1–2, 5 May 1980, Pages 128-132

    1980

  74. [83]

    Towards LHC physi cs with nonlocal Standard Model

    Tirthabir Biswas, Nobuchika Okada, “Towards LHC physi cs with nonlocal Standard Model” Available online at www.sciencedirect.com ScienceDirect , Nuclear Physics B 898 (2015) 113–131 www.elsevier.com/locate/nuclphysb

    2015

  75. [85]

    Hierarchy of Quark Mas ses, Cabibbo Angles and CP Violation,

    C. D. Froggatt and H. B. Nielsen, “Hierarchy of Quark Mas ses, Cabibbo Angles and CP Violation,” Nucl. Phys. B 147 (1979) 277–298

    1979

  76. [86]

    T he dark mat- ter interpretation of the 3.5-keV line is inconsistent with blank-sky observations

    E. Bulbul, et al., Astrophys. J. 789, 13 (2014). A. Boyarsky, O. Ruchayskiy, D. Iakubovskyi, J. Franse, Phys. Rev. Lett. 113, 251301 (2014). Christopher Dessert, Nicholas L. Rodd, Benjamin R. Safdi “T he dark mat- ter interpretation of the 3.5-keV line is inconsistent with bla...

    2014 doi arXiv

  77. [87]

    The upper right corner of the Colum bia plot with staggered fermions

    Ruben Kara, Szabolcs Borsányi, Zoltan Fodor, Jana N. Gu enther, Paolo Parotto, Attila Pasztor and Denes Sextye “The upper right corner of the Colum bia plot with staggered fermions” arXiv:2112.04192 [hep-lat] (or arXiv:2112.041 92v1 [hep-lat] for this version) https://doi.org/...

    doi arXiv

  78. [88]

    Continuum limit and universality of the Columbia plot

    Philippe de Forcrand, Massimo D’Elia “ Continuum limit and universality of the Columbia plot” arXiv:1702.00330 [hep-lat] (or arXiv:1702.00330v1 [hep-lat] for this version) https://doi.org/10.48550/arXiv.1702.00330 37 Several scales Holger Bech Nielsen

    doi arXiv

  79. [89]

    Approximate Minimal SU(5), Seve ral Fundamental Scales, Fluctuating Lattice

    Holger Bech Nielsen, “Approximate Minimal SU(5), Seve ral Fundamental Scales, Fluctuating Lattice” Proceedings of the Corfu Summer Institute 2024 "Sc hool and Workshops on Elemen- tary Particle Physics and Gravity" (CORFU2024) 12 - 26 May, and 25 August - 27 September, 2024 Co...

    2024

  80. [438]

    https://doi.org/1/zero.alt3.11/zero.alt33/PhysRevLett.32.438

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