It has been pointed out that the holonomy of generic extended loops is not gauge covariant. We show how to define a family of extended loops for which previous criticism does not apply. We also give sufficient conditions that extended loops must satisfy in order to yield covariant holonomies. This makes a quantum representation for Yang--Mills theories and gravity based on extended loops viable.

中文翻译：

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扩展完整的协方差

已经指出通用扩展循环的整体性不是规范协变的。我们展示了如何定义先前批评不适用的扩展循环系列。我们还给出了扩展循环必须满足的充分条件，以便产生协变完整。这使得基于扩展循环的杨-米尔斯理论和引力的量子表示可行。