Gross-Witten矩阵模型的非线性随机过程解
A solution of the Gross-Witten matrix model by nonlinear random processes
摘要：
本文以Gross-Witten幺正矩阵模型为例，说明了ArXiv：1009.4033中描述的求解大N量子场论中Schwinger-Dyson方程的随机方法。在强耦合极限下，该方法可以直接应用，而在弱耦合极限下，我们将变量从紧变量变为非紧变量，从而将Schwinger-Dyson方程转换为随机形式。这导致了一个新的作用量，具有无限多的高阶相互作用项。然而，这样的动作可以被有效地处理。这表明了将ArXiv：1009.4033的方法应用于具有U（N）场变量的场论以及大N极限下的有效场论的方法。
英文摘要：
We illustrate the stochastic method for solving the Schwinger-Dyson equations in large-N quantum field theories described in ArXiv:1009.4033 on the example of the Gross-Witten unitary matrix model. In the strong-coupling limit, this method can be applied directly, while in the weak-coupling limit we change the variables from compact to noncompact ones in order to cast the Schwinger-Dyson equations in the stochastic form. This leads to a new action with an infinite number of higher-order interaction terms. Nevertheless, such an action can be efficiently handled. This suggests the way to apply the method of ArXiv:1009.4033 to field theories with U(N) field variables as well as to effective field theories in the large-N limit.
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