Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1995-03-31
J.Math.Phys.37:4041-4052,1996
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Silly LaTeX error fixed so that figure is properly included
Scientific paper
10.1063/1.531615
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.
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