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.
Publication Source (Journal or Book title)
Classical and Quantum Gravity
Gambini, R., Pullin, J., & Skirzewski, A. (2021). Covariance of the extended holonomy. Classical and Quantum Gravity, 38 (2) https://doi.org/10.1088/1361-6382/abc667