A simple background-independent hamiltonian quantum model

Details A simple background-independent hamiltonian quantum model A simple background-independent hamiltonian quantum model

2003-06-13

arxiv.org/abs/gr-qc/0306059v1

Phys.Rev. D68 (2003) 104008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Scientific paper

10.1103/PhysRevD.68.104008

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.

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