AI 中文总结
该研究从格点SU(N)出发，利用Haar测度左平移不变性推导Yang-Mills理论的精确格点Dyson--Schwinger恒等式，避免李代数规范势的歧义，进而在费曼规范下得到连续极限的一点、两点连通函数方程，搭建格点恒等式与连续非微扰泛函方程的桥梁。
AI 中文摘要
我们从格点上的SU(N)出发，严格推导了连续极限下的Dyson--Schwinger方程。利用Haar测度在左群平移下的不变性，我们直接用属于SU(N)的链变量$U_μ(m)$构建了格点Yang-Mills理论的Dyson--Schwinger恒等式。这为Wilson作用量对应的主方程提供了精确的格点推导，该方程通过作用于单个链的左不变李导数来表达。由于该构建直接在紧规范群上进行，避免了在有限格点间距下引入李代数值规范势作为主要积分变量所带来的歧义。在实际应用方面，我们在第二部分通过选取费曼规范（Feynman gauge）分解了规范自由度。我们分析了所得格点恒等式的连续极限形式，并推导了一点和两点连通函数的方程。在进一步的简化约化下，这些方程闭合为一个可处理的标量系统。我们的结果在精确格点恒等式与Yang-Mills理论连续非微扰研究中常用的泛函方程之间建立了直接桥梁。
英文摘要
Starting from SU(N) on the lattice, we give a rigorous derivation of the Dyson--Schwinger equations in the continuum limit. We formulate the Dyson--Schwinger identities for the lattice Yang--Mills theory directly in terms of the link variables $U_μ(m)\in SU(N)$, exploiting the invariance of the Haar measure under left group translations. This provides an exact lattice derivation of the corresponding master equation for the Wilson action, expressed through left-invariant Lie derivatives acting on individual links. Because the construction is carried out directly on the compact gauge group, it avoids the ambiguities associated with introducing Lie-algebra valued gauge potentials as primary integration variables at finite lattice spacing. For practical applications, in a second part we then break down the gauge degree of freedom by choosing Feynman gauge. We analyze the continuum-limit form of the resulting lattice identities and derive equations for the one- and two-point connected functions. Under a further simplifying reduction, these equations close to a tractable scalar system. Our results establish a direct bridge between exact lattice identities and the functional equations commonly used in continuum nonperturbative studies of Yang--Mills theory.
Comments14 pages, 1 figure
