T₃ 涡旋三叶结模型 重子拓扑结构的几何-代数统一描述T₃ Vortex Trefoil Model Geometric-Algebraic Unified Description of Baryon Topology

Abstract This paper establishes a baryon vortex trefoil model based on the T₃ algebraic system. The T₃ three-component structure T(σ,δ,t) constructs a standard 3D Euclidean space with norm ||T|| = √(σ²+δ²+t²). By embedding standard trefoil knot parametric equations into T₃ components, a fully closed topological vortex curve is defined. Complete derived results: Velocity squared norm: ||Ṫ(u)||² = 17 + 8cos3u + 9cos²3u Total vortex arc length: L ≈ 28.84 Continuous algebraic norm distribution: N(T(u)) = −cos2u + 4cosu − 4cos4u + sin²3u, oscillates and is not constant along the curve Vacuum line tension calibrated by proton mass: λ ≈ 10.85 MeV Core conclusion: The proton is a trefoil topological vortex embedded in T₃ 3D algebraic space. Its rest mass is fully determined by the total arc length of vortex line and vacuum line tension. Color confinement originates from the inherent 3D topological non-decomposable constraint of trefoil knot, which is a geometric topological result rather than simple dynamical interaction. Keywords: T₃ algebra; trefoil knot; vortex model; baryon structure; color confinement; topological protection 摘要 本文在标准 T₃ 代数框架下建立重子的涡旋三叶结模型。T₃ 代数由三维数 T(σ, δ, t) 定义,其欧几里得模长 ||T|| = √(σ² + δ² + t²) 使分量 (σ, δ, t) 构成标准三维欧几里得空间。将三叶结参数方程嵌入 T₃ 三分量,可得到一条定义在 T₃ 空间中严格闭合的涡旋曲线。 本文完整推导得到以下定量结果: 涡旋切向量速度模长平方:||Ṫ(u)||² = 17 + 8cos3u + 9cos²3u 三叶结涡旋总弧长:L ≈ 28.84 代数范数沿涡旋曲线分布:N(T(u)) = −cos2u + 4cosu − 4cos4u + sin²3u,沿曲线非恒定振荡 真空涡旋线张力常数,由质子质量唯象标定:λ ≈ 10.85 MeV 本文核心结论:质子本质上是嵌入 T₃ 三维代数空间中的三叶结拓扑涡旋结构,其静止质量完全由涡旋线总弧长与真空线张力共同决定;强相互作用色禁闭效应,来源于三叶结固有的三维拓扑不可解约束,属于几何拓扑结果,而非单纯动力学作用。 关键词:T₃ 代数;三叶结;涡旋模型;重子结构;色禁闭;拓扑保护