Exploring the diffeomorphism invariant Hilbert space of a scalar field
arXiv:gr-qc/0609032 · doi:10.1088/0264-9381/24/18/003
Abstract
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.
arXiv comment20 pages, no figures; v3: corrected typos, added reference, some clarifications added; version as published in CQG
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- From Classical To Quantum Gravity: Introduction to Loop Quantum Gravity
- On knottings in the physical Hilbert space of LQG as given by the EPRL model
- An embedding of loop quantum cosmology in (b, v) variables into a full theory context
- Ultraviolet behavior in background independent quantum field theory
- Automorphisms in Loop Quantum Gravity
- Polymer-Fourier quantization of the scalar field revisited
- A Fock space structure for the diffeomorphism invariant Hilbert space of loop quantum gravity and its applications