Irreducibility of the Ashtekar-Isham-Lewandowski representation

Journal article
(Original article)

Publication Details

Author(s): Sahlmann H, Thiemann T
Journal: Classical and Quantum Gravity
Publisher: Institute of Physics: Hybrid Open Access
Publication year: 2006
Volume: 23
Journal issue: 13
Pages range: 4453-4471
ISSN: 0264-9381


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.

FAU Authors / FAU Editors

Sahlmann, Hanno Prof. Dr.
Professur für Theoretische Physik
Thiemann, Thomas Prof. Dr.
Chair for Theoretical Physics III (Quantum Gravity)

How to cite

Sahlmann, H., & Thiemann, T. (2006). Irreducibility of the Ashtekar-Isham-Lewandowski representation. Classical and Quantum Gravity, 23(13), 4453-4471.

Sahlmann, Hanno, and Thomas Thiemann. "Irreducibility of the Ashtekar-Isham-Lewandowski representation." Classical and Quantum Gravity 23.13 (2006): 4453-4471.


Last updated on 2018-30-10 at 20:50