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
-
95.30.Sf Relativity and gravitation
- MSC
-
83C45 Quantization of the gravitational field
47L30 Abstract operator algebras on Hilbert spaces
- Subjects
- Dates
-
Issue 3 (7 February 2008)
Received 26 August 2007, in final form 5 December 2007
Published 14 January 2008
-
The flat FRW model in LQC: self-adjointness
Wojciech Kamiński and Jerzy Lewandowski 2008 Class. Quantum Grav. 25 035001
-
An open FRW model in loop quantum cosmology
Łukasz Szulc 2007 Class. Quantum Grav. 24 6191
-
Renewal processes and fluctuation analysis of molecular motor stepping
Jaime E Santos et al 2005 Phys. Biol. 2 207
-
A classification of hidden-variable properties
Adam Brandenburger and Noson Yanofsky 2008 J. Phys. A: Math. Theor. 41 425302
-
The causal boundary of the trousers space
S G Harris and T Dray 1990 Class. Quantum Grav. 7 149
-
Statistics and geometry of cosmic voids
José Gaite JCAP11(2009)004
-
The cosmological constant problem and quintessence
Varun Sahni 2002 Class. Quantum Grav. 19 3435
-
Semiclassical states in quantum cosmology: Bianchi I coherent states
Brett Bolen et al 2004 Class. Quantum Grav. 21 4087
-
The information paradox: a pedagogical introduction
Samir D Mathur 2009 Class. Quantum Grav. 26 224001
-
On the motion of spinning test particles in plane gravitational waves
M Mohseni et al 2001 Class. Quantum Grav. 18 3007
Users also read
What's this?- Late-time tails in the Kerr spacetime
- Uniqueness of the Fock representation of the Gowdy S1 × S2 and S3 models
- A revision of the generalized uncertainty principle
Related review articles
What's this?- Loop quantum cosmology: a status report
- Tunnelling methods and Hawking's radiation: achievements and prospects
- Quantitative approaches to information recovery from black holes