When Do Measures on the Space of Connections Support the Triad Operators of Loop Quantum Gravity?
Abstract
In this work we investigate the question, under what conditions Hilbert spaces that are induced by measures on the space of generalized connections carry a representation of certain non-Abelian analogues of the electric flux. We give the problem a precise mathematical formulation and start its investigation. For the technically simple case of U(1) as gauge group, we establish a number of "no-go theorems" asserting that for certain classes of measures, the flux operators can not be represented on the corresponding Hilbert spaces. The flux-observables we consider play an important role in loop quantum gravity since they can be defined without recourse to a background geometry, and they might also be of interest in the general context of quantization of non-Abelian gauge theories.
Keywords
Cite
@article{arxiv.gr-qc/0207112,
title = {When Do Measures on the Space of Connections Support the Triad Operators of Loop Quantum Gravity?},
author = {Hanno Sahlmann},
journal= {arXiv preprint arXiv:gr-qc/0207112},
year = {2011}
}
Comments
LaTeX, 21 pages, 5 figures; v3: some typos and formulations corrected, some clarifications added, bibliography updated; article is now identical to published version