Covariance of the extended holonomy

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.

Automated summary

The holonomy of generic extended loops is not gauge covariant, but a new approach is presented in this paper to define a family of extended loops that overcomes this issue. Sufficient conditions for extended loops to yield covariant holonomies are also provided. This opens up the possibility for a quantum representation of Yang-Mills theories and gravity based on extended loops.