Abstract We develop the Diakonov - Petrov approach to the representation of the non - Abelian Wilson loop in an Abelian form. First of all, we extend this approach to the Abelian representation of the parallel transporter corresponding to the open curve rather than to the closed contour. Next, we extend this representation to the case of the non - compact groups. The obtained expressions allow us to derive the Abelian form of the Schwinger - Fock representation for the quark propagator in an external color gauge field.

中文翻译：

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阿贝尔福克 - 外规范场中夸克传播子的施温格表示

摘要 我们开发了 Diakonov - Petrov 方法来以阿贝尔形式表示非阿贝尔威尔逊环。首先，我们将这种方法扩展到对应于开放曲线而不是封闭轮廓的平行运输器的阿贝尔表示。接下来，我们将此表示扩展到非紧凑组的情况。获得的表达式使我们能够推导出外部色规场中夸克传播子的 Schwinger-Fock 表示的阿贝尔形式。