Sahlmann H (2007)
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 2007
Publisher: Institute of Physics: Hybrid Open Access
Book Volume: 24
Pages Range: 4601-4615
Journal Issue: 18
DOI: 10.1088/0264-9381/24/18/003
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.
APA:
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
MLA:
Sahlmann, Hanno. "Exploring the diffeomorphism-invariant Hilbert space of a scalar field." Classical and Quantum Gravity 24.18 (2007): 4601-4615.
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