AQV III. The holonomy-flux cross-product C*-algebra

Details AQV III. The holonomy-flux cross-product C*-algebra AQV III. The holonomy-flux cross-product C*-algebra

2011-08-19

arxiv.org/abs/1108.4579v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

49 pages, 4 figures

Scientific paper

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.

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