Diffeomorphism-invariant quantum field theories of connections in terms of webs

Journal article

Publication Details

Author(s): Lewandowski J, Thiemann T
Journal: Classical and Quantum Gravity
Publication year: 1999
Volume: 16
Journal issue: 7
Pages range: 2299-2322
ISSN: 0264-9381


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.

FAU Authors / FAU Editors

Lewandowski, Jerzy
Lehrstuhl für Theoretische Physik
Thiemann, Thomas Prof. Dr.
Lehrstuhl für Theoretische Physik

How to cite

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

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.


Last updated on 2018-10-08 at 19:53