AQV III. The holonomy-flux cross-product C*-algebra
Abstract
In this article a new C*-algebra derived from the basic quantum variables: holonomies along paths and group-valued quantum flux operators in the framework of Loop Quantum Gravity is constructed. This development is based on the theory of cross-products and C*-dynamical systems. The author has presented a set of actions of the flux group associated to a surface set on the analytic holonomy C*-algebra, which define C*-dynamical systems. These objects are used to define the holonomy-flux cross-product C*-algebra associated to a surface set. Furthermore surface-preserving path- and graph-diffeomorphism-invariant states of the new C*-algebra are analysed. Finally the holonomy-flux cross-product C*-algebra is extended such that the graph-diffeomorphisms generate among other operators the holonomy-flux-graph-diffeomorphism cross-product C*-algebra associated to a surface set.
Keywords
Cite
@article{arxiv.1108.4579,
title = {AQV III. The holonomy-flux cross-product C*-algebra},
author = {Diana Kaminski},
journal= {arXiv preprint arXiv:1108.4579},
year = {2011}
}
Comments
49 pages, 4 figures