Yang–Mills Existence and Mass Gap Proof via Topological Helicity Quantization and Beltrami Confinement under Topological Vacuum Electrodynamics
Abstract
This paper proves the existence of a four-dimensional quantum Yang–Mills theory satisfying the Osterwalder–Schrader and Wightman axioms and establishes a strictly positive mass gap Δ>0 under Topological Vacuum Electrodynamics. On the continuous electromagnetic vacuum sheet, non-Abelian gauge fields for a compact simple Lie group G arise via the Faddeev–Niemi–Cho decomposition of braided force-free Beltrami flux tubes satisfying D×Ba=α(ρ)Ba. The minor-radius cutoff a of the ground-state unknot fixes the ultraviolet phase-space capacity α−1=4π3+π2+π as a covariant curvature bound, rendering the Euclidean functional measure ultraviolet-finite while preserving full SO(4) Euclidean covariance and Lumer–Phillips reflection positivity. Helicity conservation enforces the non-linear magnetic pressure P=ξ/a4 and confining string tension √σ=2πα−1me, fixing the equilibrium tube radius a=√(ξ/σ) and evading Derrick’s scaling collapse. By Moffatt’s topological helicity quantization and the Călugăreanu–White–Fuller theorem, any non-trivial closed gauge excitation carries a strictly non-zero minimal topological linking invariant |H|≥|Hmin|>0. Applying Arnold’s ergodic helicity inequality on the self-confined Beltrami tube (where the lowest curl eigenvalue is α1=j0,1/a>0) and the global Vakulenko–Kapitanski inequality yields a strictly positive lower bound on the rest energy W≥α1/2μ0|Hmin|>0. Kato–Rellich stability against exponentially suppressed instanton tunneling rK∝ e−α−1 establishes the quantum mass gap Δ>0 and exponential clustering of vacuum correlation functions.
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BibTeX
@misc{vector2026yangmills,
title = {{Yang–Mills Existence and Mass Gap Proof via Topological Helicity Quantization and Beltrami Confinement under Topological Vacuum Electrodynamics}},
author = {Truth Vector},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23459483},
url = {https://zenodo.org/records/23459483},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Yang–Mills Existence and Mass Gap Proof via Topological Helicity Quantization and Beltrami Confinement under Topological Vacuum Electrodynamics
AU - Truth Vector
PY - 2026
DA - 2026/10/18
PB - Zenodo
DO - 10.5281/zenodo.23459483
UR - https://zenodo.org/records/23459483
AB - This paper proves the existence of a four-dimensional quantum Yang–Mills theory satisfying the Osterwalder–Schrader and Wightman axioms and establishes a strictly positive mass gap Δ>0 under Topological Vacuum Electrodynamics. On the continuous electromagnetic vacuum sheet, non-Abelian gauge fields for a compact simple Lie group G arise via the Faddeev–Niemi–Cho decomposition of braided force-free Beltrami flux tubes satisfying D×B^a=α(ρ)B^a. The minor-radius cutoff a of the ground-state unknot fixes the ultraviolet phase-space capacity α^−1=4π^3+π^2+π as a covariant curvature bound, rendering the Euclidean functional measure ultraviolet-finite while preserving full SO(4) Euclidean covariance and Lumer–Phillips reflection positivity. Helicity conservation enforces the non-linear magnetic pressure P=ξ/a^4 and confining string tension √σ=2πα^−1m_e, fixing the equilibrium tube radius a=√(ξ/σ) and evading Derrick’s scaling collapse. By Moffatt’s topological helicity quantization and the Călugăreanu–White–Fuller theorem, any non-trivial closed gauge excitation carries a strictly non-zero minimal topological linking invariant |H|≥|H_min|>0. Applying Arnold’s ergodic helicity inequality on the self-confined Beltrami tube (where the lowest curl eigenvalue is α_1=j_0,1/a>0) and the global Vakulenko–Kapitanski inequality yields a strictly positive lower bound on the rest energy W≥α_1/2μ_0|H_min|>0. Kato–Rellich stability against exponentially suppressed instanton tunneling r_K∝ e^−α^−1 establishes the quantum mass gap Δ>0 and exponential clustering of vacuum correlation functions.
ER -