楊米爾斯方程的千禧問題終於解決了: The Yang–Mills existence and mass gap problem has finally been solved

by 常 炳功, Shiqiong Wang, Shibo Chang

The Yang-Mills equations, foundational to gauge theories in particle physics, leave the origin of particle masses—particularly the mass gap in quantum chromodynamics (QCD)—unresolved, posing a central challenge in the Millennium Prize Problems. This paper introduces the Spacetime Ladder Theory, a novel framework where dark matter, as an energy-gas field, polarizes into contracting matter and expanding dark energy, driving the emergence of fundamental forces and cosmic evolution. By reformulating the Yang-Mills equations to incorporate dark matter field tensors and a dynamic dark energy term, we propose a mass generation mechanism rooted in quantized energy levels and gas induction strength. Calculations for proton (940 MeV vs. 938.272 MeV), neutron (940 MeV vs. 939.565 MeV), and glueball (1645 MeV vs. 1.2–1.7 GeV) masses show remarkable agreement with experimental data, suggesting that the coupling of dark matter polarization and dark energy expansion resolves the Yang-Mills mass gap analytically.
Conclusion The Spacetime Ladder Theory offers a compelling resolution to the Yang-Mills mass gap by attributing mass generation to dark matter polarization and dark energy expansion. Our reformulated equations and quantized energy model accurately predict hadron and glueball masses, aligning with experimental data within minimal error margins. This non-perturbative approach circumvents traditional QCD challenges, suggesting a deeper connection between cosmology and particle physics. Future work should formalize Λ(Φ), prove existence rigorously, and explore implications for cosmic evolution.
楊-米爾斯方程是描述規範場的基礎方程，廣泛應用於粒子物理學中。然而，該方程在原始形式中並未直接解釋品質的來源，尤其是在強力、弱力和電磁力的玻色子品質問題上存在未解之謎。本文從時空階梯理論的角度出發，提出了一種通過暗物質極化和暗能量膨脹機制來解決楊-米爾斯方程中品質問題的理論框架。通過改造楊-米爾斯方程，並結合氣感應強度、能級公式及量子化條件，我們提出了一種新的品質生成機制，並與實驗數據進行了對比驗證。研究表明，暗物質極化和暗能量膨脹的耦合是解釋粒子品質起源的關鍵。

149 pages, Kindle Edition

Published March 14, 2025