规范场论的研究纲领述评——一种毕达哥拉斯模式的解读

Comments on the Research Program of Gauge Field Theory——Reinterpretaion through Pythagorean Mode

宇宙的基本结构及其相互作用的奥秘都深藏于数学规律之中,这是毕达哥拉斯主义的基本理念。它分别体现在现代物理学的三大研究纲领中:(1)根据物理学的几何化纲领,引力场弯曲空间的奥秘需要通过黎曼几何、微分几何与张量分析来解读;(2)根据量子场论纲领,场理论的"产生和湮灭"算符,能方便而精确地表征和重构相关的微观作用机制;"场的本体论"和"生成辩证法"同时得到体现。(3)根据规范场论的纲领,自然界四种相互作用的奥秘都深藏于"规范对称性"之中。第三纲领相当于前两个纲领的整合。

The essence of the basic structure and interaction of cosmos are rooted in the law of mathematics which is the basic idea of Pythagoreanism. It is embodied in the three research programs of modern physics: (1) According to the program of geometrization of physics, the essence of the Curved Space in gravitational field needs to be explicated by Riemannian geometry, differential geometry, tensor analysis;(2)According to the program of quantum field theory, the generation and annihilation operator can represent and reconstruct the relevant micro-mechanism conveniently and exactly; and 'the ontology of field' and 'dialectics of generation' can both be embodied.(3) According to the program of gauge field theory, the essence of four natural interaction are rooted in 'gauge symmetry'. The third program is the combination of the former two programs.