太极统一场论(TUFT):四力职能统一的组织框架与各力标准方程的变分导出 Taiji Unified Field Theory (TUFT): An Organizational Framework for the Functional Unification of the Four Interactions and the Variational Derivation of Their Standard Equations

本文提出太极统一场论(TUFT)的第一层工作:以太极阴阳的二分、对偶、动态平衡为组织原则,将四种基本相互作用归入两类场职能——微观量子局域职能(阳)与宏观时空基底职能(阴),并以电磁相互作用作为跨尺度中介,构成四力职能闭环(此职能划分不反映电弱统一本体)。在此基础上,本文给出四力各自的标准方程,并从作用量原理出发逐一完成变分推导:引力由爱因斯坦-希尔伯特作用量变分导出爱因斯坦场方程;规范相互作用由杨-米尔斯作用量变分导出杨-米尔斯方程,QED(U(1))与 QCD(SU(3))为其特例;量子力学核心方程由各自拉格朗日密度变分导出薛定谔方程、狄拉克方程,并由正则量子化给出基本对易关系。全文所有推导均走标准作用量路径,每一步可核验。本文明确限定:太极框架承担职能分类与结构组织功能,各力方程本身以其标准形式成立,本文不宣称由太极框架推出这些方程的本体来源。双母公式直接推导路径的探索记录见附录 A,该附录不属于本文主张,不进入正文推导链。 Abstract This paper presents the first layer of the Taiji Unified Field Theory (TUFT): using the yin-yang principles of dichotomy, duality, and dynamic balance as organizational principles, the four fundamental interactions are classified into two functional categories—microscopic quantum local function (yang) and macroscopic spacetime substrate function (yin)—with the electromagnetic interaction serving as a cross-scale mediator, forming a functional closed loop among the four interactions (this functional classification does not reflect the ontological unification of the electroweak interaction). On this basis, the standard equations of the four interactions are given, and each is derived via the action principle: gravity from the Einstein-Hilbert action yields the Einstein field equation; gauge interactions from the Yang-Mills action yield the Yang-Mills equation, with QED (U(1)) and QCD (SU(3)) as special cases; the core equations of quantum mechanics are derived from their respective Lagrangian densities, yielding the Schrödinger and Dirac equations, with fundamental commutation relations from canonical quantization. All derivations follow the standard action path and are step-by-step verifiable. This paper explicitly limits the Taiji framework to functional classification and structural organization; the equations themselves hold in their standard forms, and no claim is made that the Taiji framework derives these equations' ontological origin. An exploration record of the dual master formula direct-derivation path is given in Appendix A; it does not belong to the claims of this paper and does not enter the derivation chain of the main text.