
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.
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
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
| 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). | 0 | |
| 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. | Average | |
| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Average | |
| impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Average |
