From the SP Equation to QCD
Year: 2026
Type: preprint
Abstract: Description We follow the Scretching–Planck (SP) density–phase action from quantum mechanics to the Standard Model and ask whether Yang–Mills theory is needed. The answer is that SP + non-abelian Maxwell and Yang–Mills are one set of equations, reached by two routes. The SP route derives the non-abelian field from the local SP orientation, and four measurements require its self-interaction. Every number is recomputed from CODATA and PDG inputs. One chain. The SP action ψ = √P e^{iS/ħ}, E = V + Q_SP, is exactly equivalent to Schrödinger and Heisenberg quantum mechanics. Its Fisher term gives Δx·Δp ≥ ħ/2, and its relativistic polar forms are the Klein–Gordon and Dirac (Takabayasi) equations. For hydrogen 1s the Dirac energy is −13.598468 eV and the Klein–Gordon energy −13.599193 eV; the Dirac 2p fine structure is 10.94 GHz (measured 10.969). SP + Maxwell = QED. A local phase gives minimal coupling. The Lamb shift is 1050.5 MHz at leading order (measured 1057.8), and a_e = α/2π = 0.0011614 (measured 0.0011597). SP + non-abelian Maxwell = Yang–Mills. Making the SP colour orientation local forces the field strength G = ∂A − ∂A + g f^{abc}AA. "Non-abelian Maxwell" and "Yang–Mills" denote the same field equations, here derived from SP. Do we need the non-abelian term? Yes. Without it, α_s(M_Z) = 0.904 (measured 0.1180), C_A = 0 (measured ≈ 3), σ_WW(200 GeV) = 41.2 pb (measured ≈ 17), and the proton mass is 9 MeV (measured 938). With it, all four agree: α_s(M_Z) = 0.1180, C_A = 3, σ_WW = 17.77 pb, and 938 MeV. Electroweak. The SP polar form of the Higgs doublet is the unitary gauge. It gives v = 246.22 GeV and a tree-level M_W = 79.83 GeV (measured 80.369). QCD without free quarks or gluons. Only colour singlets appear in the spectrum. Bound systems lose mass (the deuteron by 2.2246 MeV), while confined systems generate it (the proton weighs 938 MeV from about 9 MeV of quarks). The neutron–proton mass difference from the Coleman–Glashow relation is 1.229 MeV (measured 1.2933). Mass gap. On every finite lattice the gap is proved positive and equals the Poincaré constant of the SP vacuum density, Δ = λ(P₀). It is computed in SU(2), SU(3), Migdal–Kadanoff and O(N) models. The continuum statement (Conjecture C) remains the open Clay problem. Both SP branches. The Wronskian of the two SP solutions gives the deuteron. From scattering data alone it yields B = 2.2266 MeV (measured 2.2246) and the deuteron mass to within 2 keV. It also gives η = 0.0257 (measured 0.0256) and a no-threshold lemma for confinement. The paper includes 51 solved problems, with all code and data. Keywords: Scretching–Planck; density–phase action; Schrödinger; Heisenberg; Klein–Gordon; Dirac; QED; non-abelian Maxwell; Yang–Mills; electroweak; Higgs; QCD; mass gap; Poincaré constant; deuteron; two branches
Author: Scretching, Daniel
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225201778