In diffeomorphism-invariant models, invariant content requires spatiotemporal structures beyond correlations, as correlations are invariant only in a generalized non-smooth sense and spatiotemporal relations are also invariant.
A simple background-independent hamiltonian quantum model
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abstract
We study formulation and probabilistic interpretation of a simple general-relativistic hamiltonian quantum system. The system has no unitary evolution in background time. The quantum theory yields transition probabilities between measurable quantities (partial observables). These converge to the classical predictions in the $\hbar\to 0$ limit. Our main tool is the kernel of the projector on the solutions of Wheeler-deWitt equation, which we analyze in detail. It is a real quantity, which can be seen as a propagator that propagates "forward" as well as "backward" in a local parameter time. Individual quantum states, on the other hand, may contain only "forward propagating" components. The analysis sheds some light on the interpretation of background independent transition amplitudes in quantum gravity.
fields
gr-qc 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Diffeomorphism-Invariant Quantities in Phase Space: More than Correlations
In diffeomorphism-invariant models, invariant content requires spatiotemporal structures beyond correlations, as correlations are invariant only in a generalized non-smooth sense and spatiotemporal relations are also invariant.