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 γ parameter in controlling spacetime discreteness. In this way, standard quantum cosmology is shown to be the simultaneous limit γ → 0, j → ∞ 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 ℏ → 0, l → ∞ of angular momentum in quantum mechanics. Possible lessons for semiclassical states at the dynamical level in the full theory of quantum geometry are mentioned.
All Science Journal Classification (ASJC) codes
- Physics and Astronomy (miscellaneous)