Observables and a Hilbert Space for Bianchi IX

Details Observables and a Hilbert Space for Bianchi IX Observables and a Hilbert Space for Bianchi IX

1994-09-23

arxiv.org/abs/gr-qc/9409049v1

Class.Quant.Grav.12:1441-1454,1995

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

23 pages, ReVTeX, CGPG-94/6-3, UCSBTH-94-39

Scientific paper

10.1088/0264-9381/12/6/010

We consider a quantization of the Bianchi IX cosmological model based on taking the constraint to be a self-adjoint operator in an auxiliary Hilbert space. Using a WKB-style self-consistent approximation, the constraint chosen is shown to have only continuous spectrum at zero. Nevertheless, the auxiliary space induces an inner product on the zero-eigenvalue generalized eigenstates such that the resulting physical Hilbert space has countably infinite dimension. In addition, a complete set of gauge-invariant operators on the physical space is constructed by integrating differential forms over the spacetime. The behavior of these operators indicates that this quantization preserves Wald's classical result that the Bianchi IX spacetimes expand to a maximum volume and then recollapse.

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