Non-covariance of the generalized holonomies: Examples
Abstract
A key aspect of a recent proposal for a {\em 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 {\em 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 {\em not} covariant with respect to small gauge transformations; their traces are {\em not} observables of the gauge theory. This result indicates what may be a serious complication to the use of generalized loops in physics.
Keywords
Cite
@article{arxiv.gr-qc/9503064,
title = {Non-covariance of the generalized holonomies: Examples},
author = {Troy A. Schilling},
journal= {arXiv preprint arXiv:gr-qc/9503064},
year = {2010}
}
Comments
Silly LaTeX error fixed so that figure is properly included