AQV II. A new formulation of the Weyl C*-algebra

Details AQV II. A new formulation of the Weyl C*-algebra AQV II. A new formulation of the Weyl C*-algebra

2011-08-19

arxiv.org/abs/1108.4578v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

71 pages, 10 figures

Scientific paper

In this article a new formulation of the Weyl C*-algebra, which has been invented by Fleischhack, in terms of C*-dynamical systems is presented. The quantum configuration variables are given by the holonomies along paths in a graph. Functions depending on these quantum variables form the analytic holonomy C*-algebra. Each classical flux variable is quantised as an element of a flux group associated to a certain surface set and a graph. The quantised spatial diffeomorphisms are elements of the group of bisections of a finite graph system. Then different actions of the flux group associated to surfaces and the group of bisections on the analytic holonomy C*-algebra are studied. The Weyl C*-algebra for surfaces is generated by unitary operators, which implements the group-valued quantum flux operators, and certain functions depending on holonomies along paths that satisfy canonical commutation relations. Furthermore there is a unique pure state on the commutative Weyl C*-algebra for surfaces, which is a path- or graph-diffeomorphism invariant.

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