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ID: 50999.0, MPI für Gravitationsphysik / Quantum Gravity and Unified Theories
Irreducibility of the Ashtekar-Isham-Lewandowski representation
Authors:Sahlmann, Hanno; Thiemann, Thomas
Language:English
Date of Publication (YYYY-MM-DD):2006
Title of Journal:Classical and Quantum Gravity
Volume:23
End Page:4453
Sequence Number of Article:4472
Review Status:not specified
Audience:Not Specified
Abstract / Description: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.
External Publication Status:published
Document Type:Article
Communicated by:Hermann Nicolai
Affiliations:MPI für Gravitationsphysik/Quantum Gravity and Unified Theories
Identifiers:URL:http://www.iop.org/EJ/abstract/0264-9381/23/13/010
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