Non-covariance of the generalized holonomies: Examples

الأصل · EN

A key aspect of a recent proposal for a generalized loop representation of quantum Yang-Mills theory and gravity is considered. Such a representation of the quantum theory has been expected to arise via consideration of a particular algebra of observables -- given by the traces of the holonomies of generalized loops. We notice, however, a technical subtlety, which prevents us from reaching the conclusion that the generalized holonomies are covariant with respect to small gauge transformations. Further analysis is given which shows that they are not covariant with respect to small gauge transformations; their traces are not observables of the gauge theory. This result indicates what may be a serious complication to the use of generalized loops in physics.