On the Configuration Spaces of Homogeneous Loop Quantum Cosmology and Loop Quantum Gravity

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dc.creatorBrunnemann, Johannes
dc.creatorFleischhack, Christian
dc.date2007-09-11
dc.date2009-04-24
dc.date.accessioned2026-07-07T13:07:26Z
dc.date.available2026-07-07T13:07:26Z
dc.descriptionThe set of homogeneous isotropic connections, as used in loop quantum cosmology, forms a line $l$ in the space of all connections $\cal A$. This embedding, however, does not continuously extend to an embedding of the configuration space $\overline l$ of homogeneous isotropic loop quantum cosmology into that of loop quantum gravity, $\overline{\cal A}$. This follows from the fact that the parallel transports for general, non-straight paths in the base manifold do not depend almost periodically on $l$. Analogous results are given for the anisotropic case.
dc.description12 pages, LaTeX. v1 to v2: Results unchanged. Presentation improved: Sect. 4 restructured (proof of Cor. 4.5 as well); some comments added; reference updated
dc.identifierhttps://arxiv.org/abs/0709.1621
dc.identifierhttp://arxiv.org/abs/0709.1621
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/228090
dc.subjectMathematical Physics
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subject34C27 (Primary) 53C05, 83F05 (Secondary)
dc.titleOn the Configuration Spaces of Homogeneous Loop Quantum Cosmology and Loop Quantum Gravity
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