Lewandowski J, Thiemann T (1999)
Publication Status: Published
Publication Type: Journal article
Publication year: 1999
Publisher: IOP PUBLISHING LTD
Book Volume: 16
Pages Range: 2299-2322
Journal Issue: 7
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.
APA:
Lewandowski, J., & Thiemann, T. (1999). Diffeomorphism-invariant quantum field theories of connections in terms of webs. Classical and Quantum Gravity, 16(7), 2299-2322.
MLA:
Lewandowski, Jerzy, and Thomas Thiemann. "Diffeomorphism-invariant quantum field theories of connections in terms of webs." Classical and Quantum Gravity 16.7 (1999): 2299-2322.
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