Exploring the diffeomorphism-invariant Hilbert space of a scalar field

Journal article
(Original article)

Publication Details

Author(s): Sahlmann H
Journal: Classical and Quantum Gravity
Publisher: Institute of Physics: Hybrid Open Access
Publication year: 2007
Volume: 24
Journal issue: 18
Pages range: 4601-4615
ISSN: 0264-9381


As a toy model for the implementation of the diffeomorphism constraint, the interpretation of the resulting states and the treatment of ordering ambiguities in loop quantum gravity, we consider the Hilbert space of spatially diffeomorphism-invariant states for a scalar field. We give a very explicit formula for the scalar product on this space and discuss its structure. Then we turn to the quantization of a certain class of diffeomorphism-invariant quantities on that space and discuss in detail the ordering issues involved. On a technical level these issues bear some similarity to those encountered in full loop quantum gravity. © 2007 IOP Publishing Ltd.

FAU Authors / FAU Editors

Sahlmann, Hanno Prof. Dr.
Professur für Theoretische Physik

How to cite

Sahlmann, H. (2007). Exploring the diffeomorphism-invariant Hilbert space of a scalar field. Classical and Quantum Gravity, 24(18), 4601-4615. https://dx.doi.org/10.1088/0264-9381/24/18/003

Sahlmann, Hanno. "Exploring the diffeomorphism-invariant Hilbert space of a scalar field." Classical and Quantum Gravity 24.18 (2007): 4601-4615.


Last updated on 2018-30-10 at 13:50