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2007

The flat FRW model in LQC: the self-adjointness

Kamiński, Wojciech, Lewandowski, Jerzy

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The flat FRW model coupled to the massless scalar field according to the improved, background scale independent version of Ashtekar, Pawlowski and Singh is considered.

The core of the theory is addressed directly: the APS construction of the quantum Hamiltonian is analyzed under the assumption that cosmological constant $\Lambda\le 0$.
We prove the essential self-adjointness of the operator whose square-root defines the quantum Hamiltonian operator and therefore, provide the explicit definition.
If $\Lambda<0$, then the spectrum is discrete.

The flat FRW model in LQC: the self-adjointness · Around

Built on

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Kato T 1980, Perturbation Theory for Linear Operators, (Springer-Verlag)
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Bojowald M 2001, Loop quantum cosmology: III. Wheeler-DeWitt operators, Class. Quantum Grav. 18
2003
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Rovelli C 2004, Quantum Gravity, (Cambridge Cambridge University Press) Thiemann T, Introduction to Modern Canonical Quantum General Relativity (Cambridge: Cambridge University Press), Ashtekar A and Lewandowski J 2004, Background independent quantum gravity: A status report, Class. Quant. Grav. 21
2004
Earlier work this paper cites.

Similar

Ashtekar A, Pawłowski T and Singh P 2006, Quantum Nature of Big Bang: Improved dynamics, Phys. Rev. D 7
2006
Cited alongside, same era.
Kamiński W, Lewandowski J, Pawłowski T and Szulc Ł 2006, Properties of the scalar constraint operator in LQC models, in preparation
2006
Cited alongside, same era.
Ashtekar A, Pawłowski T, Vandersloot K and Singh P 2006 Loop quantum cosmology of k = 1 k=1 FRW models 2007 Phys.Rev. D
2007
Cited alongside, same era.

Then

Vandersloot K 2006, Loop quantum cosmology and the k = - 1 RW model, Preprint gr-qc/0612070 Szulc L 2007 Open FRW model in Loop Quantum Cosmology, gr-qc/0612101
2007
Closest in time.
Astekar A, Corichi A, Singh P 2007, contributed talk at IGC Inaugural Conference Aug 9-11, 2007, Penn State
2007
Closest in time.
Pawłowski T, contributed talk at IGC Inaugural Conference Aug 9-11, 2007, Penn State
2007
Closest in time.

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