2006/09/30 by Hanno Sahlmann · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/0264-9381/24/18/003
published as Class.Quant.Grav.24:4601-4616,2007 · 20 pages, no figures; v3: corrected typos, added reference, some clarifications added; version as published in CQG
openalex publication_date 2007/08/30 · arxiv created 2007/08/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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.