Diffeomorphism-invariant quantum field theories of connections in terms of webs
- 1 January 1999
- journal article
- Published by IOP Publishing in Classical and Quantum Gravity
- Vol. 16 (7), 2299-2322
- https://doi.org/10.1088/0264-9381/16/7/311
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.This publication has 28 references indexed in Scilit:
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