Superselection sectors in the Ashtekar-Horowitz-Boulware model

Abstract

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/(2π\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.

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

References in corpus (15)

• Quantization of diffeomorphism invariant theories of connections with local degrees of freedom
• Quantum Observables and Recollapsing Dynamics
• On the Generality of Refined Algebraic Quantization
• A Uniqueness Theorem for Constraint Quantization
• An algebraic extension of Dirac quantization: Examples
• Refined Algebraic Quantization: Systems with a single constraint
• Solution space of 2+1 gravity on $\mathbf{R}\times T^2$ in Witten's connection formulation
• Group Averaging and Refined Algebraic Quantization: Where are we now?
• Refined Algebraic Quantization in the oscillator representation of SL(2,R)
• Group Averaging and Refined Algebraic Quantization
• On Group Averaging for SO(n,1)
• An algebraic approach to the quantization of cosntrained systems: finite dimensional examples
• Group averaging in the (p,q) oscillator representation of SL(2,R)
• The quantization of constrained systems: from symplectic reduction to Rieffel induction
• Refined algebraic quantisation with the triangular subgroup of SL(2,R)

Cited by in corpus (12)

• Observables in effective gravity
• Group Averaging for de Sitter free fields
• A global picture of quantum de Sitter space
• Group averaging, positive definiteness and superselection sectors
• Solving the Problem of Time in Mini-superspace: Measurement of Dirac Observables
• Group Averaging of massless scalar fields in 1+1 de Sitter
• Highly Irregular Quantum Constraints
• Deformation quantization of constrained systems: a group averaging approach
• Constraint rescaling in refined algebraic quantisation: momentum constraint
• Refined algebraic quantisation in a system with nonconstant gauge invariant structure functions
• The Projection Operator Method and the Ashtekar-Horowitz-Boulware Model
• Supergravity on a 3-torus: quantum linearization instabilities with a supergroup