Sahlmann H, Thiemann T (2006)
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 2006
Publisher: Institute of Physics: Hybrid Open Access
Book Volume: 23
Pages Range: 4453-4471
Article Number: 010
Journal Issue: 13
DOI: 10.1088/0264-9381/23/13/010
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 (AIL) representation, has been constructed. Recently, several uniqueness results for this representation have been worked out. In the present paper, 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. © 2006 IOP Publishing Ltd.
APA:
Sahlmann, H., & Thiemann, T. (2006). Irreducibility of the Ashtekar-Isham-Lewandowski representation. Classical and Quantum Gravity, 23(13), 4453-4471. https://dx.doi.org/10.1088/0264-9381/23/13/010
MLA:
Sahlmann, Hanno, and Thomas Thiemann. "Irreducibility of the Ashtekar-Isham-Lewandowski representation." Classical and Quantum Gravity 23.13 (2006): 4453-4471.
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