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ZENODO
Dataset . 2026
License: CC BY
Data sources: Datacite
ZENODO
Dataset . 2026
License: CC BY
Data sources: Datacite
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Electromagnetism and Quantum Chromodynamics in Noncommutative Spectral Geometry: From Waves and Solitons to Confinement

Authors: Valeri Vukolov;

Electromagnetism and Quantum Chromodynamics in Noncommutative Spectral Geometry: From Waves and Solitons to Confinement

Abstract

We present a comprehensive analysis of electromagnetic and strong interactions within the framework of noncommutative spectral geometry, where gauge fields are identified with spacetime contorsion. This geometric unification reveals that all elementary particles — leptons, quarks, photons, gluons — are different manifestations of the same fundamental object: the axial vortex.Key results include:1. Electromagnetic sector: Photons emerge as spherical torsion waves propagating along generalized geodesics. The fundamental relations E ⊥ B ⊥ k are preserved as geometric necessities, but the vacuum impedance becomes energy-dependent: Z0(ω) = Z (0) 0 [1 − α 2(ω/ΛNC)2]. The Coulomb potential acquires a contact term: ϕ(r) = 14πϵ0 q r[1 + θ2 2 δ3(r)], regularizing the classi-cal singularity. Light cones become energy-dependent ("rainbow geometry"), yet microcausality is rigorously preserved. Like Born-Infeld theory, our model forbids electromagnetic shock waves.2. Strong interaction sector: Quarks are described as tori T 2 with non-trivial SU(3) bundles classified by the first Chern class c1 ∈ Z3. Gluons are spherical torsion waves in the SU(3) sector, propagating with a modified dispersion relation. Quark-gluon interactions occur through topological resonance conditions analogous to the photoelectric effect, with color conservation enforced by ∆c1 = ±1.3. Confinement: The energy required to separate two colored tori with total Chern class ctotal1 ̸= 0 mod 3 grows linearly with distance, producing a stringtension σ = g23 8π ln(Rcut/Rc) ≈ 0.18 GeV2, matching lattice QCD results. This is a topological necessity, not a dynamical accident.4. Nucleons as bound states: A proton or neutron is the connected sum of three quark tori, Σ3 = T 2#T 2#T 2, a genus-3 surface whose topological structure explains confinement and proton stability. The color singlet condition c1 + c2 + c3 = 0 mod 3 ensures the total SU(3) bundle is trivial.5. Unification: All particles emerge from the same spectral triple (A, H, D, J,γ) with finite algebra AF = C ⊕ H ⊕ M3(C). The differences between electrons, quarks, photons, and gluons are merely different projections in the gauge indices and the effective scale ϕeff0 All modifications are controlled by the noncommutativity scale ΛNC ∼ 1016 GeV,ensuring consistency with all current experiments while making testable predictions for future high-energy and astrophysical observations.

Keywords

noncommutative geometry, spectral triple, electromagnetism, quantum chromodynamics, QCD, torsion, contorsion, axial vortex, photon, gluon, quark, confinement, string tension, Born-Infeld theory, spectral action, Standard Model, topological soliton, noncommutative torus, Chern class, nucleon, proton stability, quark-gluon plasma, rainbow geometry, modified dispersion relation

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average