平面上Yang-Mills理论的随机Feynman规则
Stochastic Feynman Rules for Yang-Mills Theory on the Plane
摘要：
我们分析量子杨米尔斯理论$\mathbb{R}^2$使用一种新的离散化方法的基础上的代数模拟的随机微积分。这样的类比涉及使用“高斯”自由场，其协方差矩阵是不定的而不是正定的。具体来说，我们的工作与李代数价值领域的晶格和利用近似规范不变性时恢复的连续极限。这种分析被施加到显示之间的等价性威尔逊圈的期望值计算使用部分轴向规范，完全轴向规范，和Migdal-Witten格公式。因此，我们获得了涉及热核和迭代积分的有趣的李理论等式。
英文摘要：
We analyze quantum Yang-Mills theory on $\mathbb{R}^2$ using a novel discretization method based on an algebraic analogue of stochastic calculus. Such an analogue involves working with "Gaussian" free fields whose covariance matrix is indefinite rather than positive definite. Specifically, we work with Lie-algebra valued fields on a lattice and exploit an approximate gauge-invariance that is restored when taking the continuum limit. This analysis is applied to show the equivalence between Wilson loop expectations computed using partial axial-gauge, complete axial-gauge, and the Migdal-Witten lattice formulation. As a consequence, we obtain intriguing Lie-theoretic identities involving heat kernels and iterated integrals.
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