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Journal Article

#### Irreducibility of the Ashtekar-Isham-Lewandowski representation

##### Fulltext (public)

50999.pdf

(Preprint), 202KB

##### Supplementary Material (public)

There is no public supplementary material available

##### Citation

Sahlmann, H., & Thiemann, T. (2006). Irreducibility of the Ashtekar-Isham-Lewandowski
representation.* Classical and Quantum Gravity,* *23*: 4472.
4453. Retrieved from http://www.iop.org/EJ/abstract/0264-9381/23/13/010.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-4AD1-3

##### Abstract

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.