平面上杨-米尔斯理论的马氏方程的三种证明
Three proofs of the Makeenko-Migdal equation for Yang-Mills theory on the plane
摘要：
我们给出了平面上杨-米尔斯测度的马氏-米格达尔方程的三个简短证明，两个使用边缘变量，一个使用循环或套索变量。我们的证明比T. Lévy和A.达尔奎斯特特别是，我们的证明是“本地”的性质，因为它们只涉及衍生物的变量相邻的交叉问题。在一篇与F.加布里埃尔，我们将表明，我们的两个证明可以适应的情况下，杨米尔斯理论在一个紧凑的表面。
英文摘要：
We give three short proofs of the Makeenko-Migdal equation for the Yang-Mills measure on the plane, two using the edge variables and one using the loop or lasso variables. Our proofs are significantly simpler than the earlier pioneering rigorous proofs given by T. Lévy and by A. Dahlqvist. In particular, our proofs are "local" in nature, in that they involve only derivatives with respect to variables adjacent to the crossing in question. In an accompanying paper with F. Gabriel, we will show that two of our proofs can be adapted to the case of Yang-Mills theory on a compact surface.
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