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  Diffeomorphism invariant quantum field theories of connections in terms of webs

Lewandowski, J., & Thiemann, T. (1999). Diffeomorphism invariant quantum field theories of connections in terms of webs. Classical and Quantum Gravity, 16(7), 2299-2322.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-58CE-D Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-58CF-B
Genre: Journal Article

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Lewandowski, Jerzy1, 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: In the canonical quantization of gravity in terms of the Ashtekar variables one uses paths in the 3-space to construct the quantum states. Usually, one restricts oneself to families of paths admitting only a finite number of isolated intersections. This assumption implies a limitation on the diffeomorphisms invariance of the introduced structures. In this work, using the previous results of Baez and Sawin, we extend the existing results to a theory admitting all the possible piecewise-smooth finite paths and loops. In particular, we (a) characterize the spectrum of the Ashtekar-Isham configuration space, (b) introduce spin-web states, a generalization of the spin-network states, (c) extend the diffeomorphism averaging to the spin-web states and derive a large class of diffeomorphism-invariant states and finally (d) extend the 3-geometry operators and the Hamiltonian operator.

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 Dates: 1999
 Publication Status: Published in print
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 Identifiers: eDoc: 206203
Other: 16431
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Title: Classical and Quantum Gravity
Source Genre: Journal
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Pages: - Volume / Issue: 16 (7) Sequence Number: - Start / End Page: 2299 - 2322 Identifier: -