Superselection sectors in the Ashtekar-Horowitz-Boulware model

Details Superselection sectors in the Ashtekar-Horowitz-Boulware model Superselection sectors in the Ashtekar-Horowitz-Boulware model

2005-05-19

arxiv.org/abs/gr-qc/0505097v3

Class.Quant.Grav. 22 (2005) 4007-4020

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

17 pages, latex with amsfonts, amsmath, amssymb. (v3: Clarifying comments added.)

Scientific paper

10.1088/0264-9381/22/19/012

We investigate refined algebraic quantisation of the constrained Hamiltonian system introduced by Boulware as a simplified version of the Ashtekar-Horowitz model. The dimension of the physical Hilbert space is finite and asymptotes in the semiclassical limit to 1/(2\pi\hbar) times the volume of the reduced phase space. The representation of the physical observable algebra is irreducible for generic potentials but decomposes into irreducible subrepresentations for certain special potentials. The superselection sectors are related to singularities in the reduced phase space and to the rate of divergence in the formal group averaging integral. There is no tunnelling into the classically forbidden region of the unreduced configuration space, but there can be tunnelling between disconnected components of the classically allowed region.

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