Wojciech Kamiński and Jerzy Lewandowski 2008 Class. Quantum Grav. 25 035001 doi:10.1088/0264-9381/25/3/035001
The flat FRW model in LQC: self-adjointness
Wojciech Kamiński and Jerzy Lewandowski
Show affiliationsThe flat Friedman–Robertson–Walker (FRW) model coupled to the massless scalar field according to the improved, background scale-independent version of Ashtekar, Pawłowski and Singh [1] is considered. The core of the theory is addressed directly: the APS construction of the quantum Hamiltonian is analyzed under the assumption that the cosmological constant Λ ≤ 0. We prove the essential self-adjointness of the operator whose square-root defines in [1] the quantum Hamiltonian operator and therefore provide the explicit definition. If Λ < 0, then the spectrum is discrete. In the Λ = 0 case, the essential and absolutely continuous spectra of the operator are derived. The latter operator is related in the unitary way to the absolutely continuous part of the quantum mechanics operator 
(a, b > 0 being some constants) plus a trace class operator.
- PACS
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95.30.Sf Relativity and gravitation
- MSC
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83C45 Quantization of the gravitational field
47L30 Abstract operator algebras on Hilbert spaces
- Subjects
- Dates
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Issue 3 (7 February 2008)
Received 26 August 2007, in final form 5 December 2007
Published 14 January 2008
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The flat FRW model in LQC: self-adjointness
Wojciech Kamiński and Jerzy Lewandowski 2008 Class. Quantum Grav. 25 035001
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