A length operator for canonical quantum gravity

Journal article

Publication Details

Author(s): Thiemann T
Journal: Journal of Mathematical Physics
Publication year: 1998
Volume: 39
Journal issue: 6
Pages range: 3372-3392
ISSN: 0022-2488


We construct an operator that measures the length of a curve in four-dimensional Lorentzian vacuum quantum gravity. We work in a representation in which an SU(2) connection is diagonal and it is therefore surprising that the operator obtained after regularization is densely defined, does not suffer from factor ordering singularities, and does not require any renormalization. We show that the length operator admits self-adjoint extensions and compute part of its spectrum which, like its companions, the volume and area operators already constructed in the literature, is purely discrete and roughly quantized in units of the Planck length. The length operator contains full and direct information about all the components of the metric tensor which facilitates the construction of so-called weave states which approximate a given classical three-geometry. (C) 1998 American Institute of Physics.

FAU Authors / FAU Editors

Thiemann, Thomas Prof. Dr.
Lehrstuhl für Theoretische Physik

How to cite

Thiemann, T. (1998). A length operator for canonical quantum gravity. Journal of Mathematical Physics, 39(6), 3372-3392.

Thiemann, Thomas. "A length operator for canonical quantum gravity." Journal of Mathematical Physics 39.6 (1998): 3372-3392.


Last updated on 2018-08-08 at 16:38