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  On the superselection theory of the Weyl algebra for diffeomorphism invariant quantum gauge theories

Sahlmann, H., & Thiemann, T. (2003). On the superselection theory of the Weyl algebra for diffeomorphism invariant quantum gauge theories.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-52E0-6 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-52E1-4
Genre: Journal Article

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50973.pdf (Preprint), 386KB
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 Creators:
Sahlmann, Hanno, Author
Thiemann, Thomas1, Author              
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1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              

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 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-Lewandowski representation, has been constructed. This representation is singled out by its mathematical elegance, and up to now, no other diffeomorphism invariant representation has been constructed. This raises the question whether it is unique in a precise sense. In the present article we take steps towards answering this question. Our main result is that upon imposing relatively mild additional assumptions, the AL-representation is indeed unique. As an important tool which is also interesting in its own right, we introduce a C -algebra which is very similar to the Weyl algebra used in the canonical quantization of free quantum field theories.

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 Dates: 2003
 Publication Status: Published in print
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 Identifiers: eDoc: 50973
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