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Journal Article

Irreducibility of the Ashtekar-Isham-Lewandowski representation

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Thiemann,  Thomas
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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(Preprint), 202KB

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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.