AQV IV. A new formulation of the holonomy-flux *-algebra

Details AQV IV. A new formulation of the holonomy-flux *-algebra AQV IV. A new formulation of the holonomy-flux *-algebra

2011-08-19

arxiv.org/abs/1108.4580v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

46 pages, 7 figures

Scientific paper

In this article the holonomy-flux *-algebra, which has been introduced by Lewandowski, Okolow, Sahlmann and Thiemann, is modificated. The new *-algebra is called the holonomy-flux cross-product *-algebra. This algebra is an abstract cross-product *-algebra. It is given by the universal algebra of the algebra of continuous and differentiable functions on the configuration space of generalised connections and the universal enveloping flux algebra associated to a surface set, and some canonical commutator relations. There is a uniqueness result for a certain path- and graph-diffeomorphism invariant state of the holonomy-flux cross-product *-algebra. This new *-algebra is not the only *-algebra, which is generated by the algebra of certain continuous and differentiable functions on the configuration space of generalised connections and the universal enveloping flux algebra associated to a surface set. The theory of abstract cross-product algebras allows to define different new *-algebras. Some of these algebras are presented in this article.

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