Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2003-03-20
Class.Quant.Grav. 23 (2006) 4453-4472
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
13 pages, no figures
Scientific paper
Much of the work in loop quantum gravity and quantum geometry rests on a mathematically rigorous integration theory on spaces of distributional connections. Most notably, a diffeomorphism invariant representation of the algebra of basic observables of the theory, the Ashtekar-Isham-Lewandowski representation, has been constructed. Recently, several uniqueness results for this representation have been worked out. In the present article, we contribute to these efforts by showing that the AIL-representation is irreducible, provided it is viewed as the representation of a certain C*-algebra which is very similar to the Weyl algebra used in the canonical quantization of free quantum field theories.
Sahlmann Hanno
Thiemann Thomas
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