空间引导场理论：从梯度假设和电荷守恒到规范群结构
Spatial Guidance Field Theory: From Gradient Postulates and Charge Conservation to Gauge Group Structure
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中文总结 AI 辅助
本文从两个基本假设构建统一相互作用理论，推导内部对称群为紧致李群，在相关要求下挑选出标准模型规范群，给出强、弱相互作用描述及可测试信号，还探讨对黑洞物理的影响，提供对标准模型规范结构的第一性原理理解。
中文摘要 AI 辅助
我们从两个基本假设构建了一个统一的相互作用理论：（1）所有基本力都作为引导势的梯度出现，（2）产生这些势的电荷是守恒的。在非相对论极限下，标量引导场重现牛顿引力和库仑定律。相对论一致性迫使引导势升级为时空度规和规范矢量场。本文的核心进展是严格推导内部对称群必须是紧致李群；结合手征费米子的反常消除，这种紧致性严重限制了允许的规范群。在最小秩和表示内容的额外要求下，该框架唯一地挑选出标准模型的\(SU(3)_c \times SU(2)_L \times U(1)_Y\)作为所有紧致无反常群中最经济的选择。该框架因此提供了对标准模型规范结构的第一性原理理解。我们还给出了强相互作用和弱相互作用的引导场描述，并讨论了可测试信号，如由引导势的非线性叠加引起的等效原理违反。作为应用，我们探索了对黑洞物理学的影响，其中引导视角暗示了与色禁闭的对偶性和避免奇点的自然机制，在引力波衰减中可能有观测特征。
英文摘要
We construct a unified framework for interactions from three postulates: (1) all elementary forces arise as gradients of guidance potentials, (2) the charges that generate these potentials are conserved, and (3) the internal symmetry group must accommodate chiral fermions. The chirality postulate forces the internal symmetry group to be non-Abelian. In the non-relativistic limit, a scalar guidance field reproduces Newtonian gravity and Coulomb's law, and relativistic consistency upgrades the potentials to a spacetime metric and gauge vector fields. The central result is a rigorous derivation that the internal symmetry group must be a compact Lie group; combined with anomaly cancellation and minimal rank and representation content, this uniquely selects the Standard Model's $SU(3)_c \times SU(2)_L \times U(1)_Y$. We present a guidance-field description of strong and weak interactions, and derive coupling-modified Tolman--Oppenheimer--Volkoff equations for neutron stars, obtaining a theoretical maximum mass of $M_{\rm max}^{\rm th} \approx 2.8 \pm 0.4\,M_\odot$, naturally accommodating the $2.6\,M_\odot$ companion of GW190814. We further derive quantitative predictions for equivalence principle violation from nonlinear superposition of guidance potentials, with a QCD-scale benchmark within reach of next-generation experiments. Finally, we discuss implications for black hole interiors within a geometric framework in which charges are topological invariants of a generalized space, and provide the mathematical formulation of the total connection, its action functional, and field equations.
