The Semiclassical Limit of Loop Quantum Cosmology

Abstract

The continuum and semiclassical limits of isotropic, spatially flat loop quantum cosmology are discussed, with an emphasis on the role played by the Barbero-Immirzi parameter γin controlling space-time discreteness. In this way, standard quantum cosmology is shown to be the simultaneous limit γ\to 0, j \to \infty of loop quantum cosmology. Here, j is a label of the volume eigenvalues, and the simultaneous limit is technically the same as the classical limit \hbar \to 0, l \to \infty of angular momentum in quantum mechanics. Possible lessons for semiclassical states at the dynamical level in the full theory of quantum geometry are mentioned.

10 pages

References in corpus (6)

• Absence of Singularity in Loop Quantum Cosmology
• Isotropic Loop Quantum Cosmology
• Coherent States for Canonical Quantum General Relativity and the Infinite Tensor Product Extension
• Dynamical Initial Conditions in Quantum Cosmology
• Photons from quantized electric flux representations
• Statistical geometry of random weave states

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