Title: The Geometrical Basis of the Nonlinear Gauge Show Chinese title

Title: 非线性规范的几何基础

Abstract: We consider Yang-Mills theory in Euclidean space-time $(R^4)$ and construct its configuration space. The orbits are first shown to form a congruence set. Then we discuss the orthogonal gauge condition in Abelian theory and show that Coulomb-like surfaces foliate the entire configuration space. In the non-Abelian case, where these exists no global orthogonal gauge, we derive the non-linear gauge proposed previously by the author by modifying the orthogonality condition. However, unlike the Abelian case, the entire configuration space cannot be foliated by submanifolds defined by the non-linear gauge. The foliation is only limited to the non-perturbative regime of Yang-Mills theory. Show Chinese abstract

Abstract: 我们考虑欧几里得时空中的杨-米尔斯理论$(R^4)$并构建其配置空间。 这些轨道首先被证明形成一个同余集。 然后我们讨论阿贝尔理论中的正交规范条件，并表明 库仑类似曲面对整个配置空间进行分层。 在非阿贝尔情况下，由于不存在全局正交规范，我们通过修改正交性条件推导出作者之前提出的非线性规范。 然而，与阿贝尔情况不同，整个配置空间不能由由非线性规范定义的子流形进行分层。 该分层仅限于杨-米尔斯理论的非微扰区域。