Kinematical Foundations of Loop Quantum Cosmology

Christian Fleischhack ()
Additional contact information
Christian Fleischhack: Universität Paderborn, Institut für Mathematik

A chapter in Quantum Mathematical Physics, 2016, pp 201-232 from Springer

Abstract: Abstract First, we review the C ∗-algebraic foundations of loop quantization, in particular, the construction of quantum configuration spaces and the implementation of symmetries. Then, we apply these results to loop quantum gravity, focusing on the space of generalized connections and on measures thereon. Finally, we study the realm of homogeneous isotropic loop quantum cosmology: once viewed as the loop quantization of classical cosmology, once seen as the symmetric sector of loop quantum gravity. It will turn out that both theories differ, i.e., quantization and symmetry reduction do not commute. Moreover, we will present a uniqueness result for kinematical measures. These last two key results have originally been due to Hanusch; here, we give drastically simplified and direct proofs.

Keywords: Loop quantization; Gravity; Cosmology; Abelian C ∗ algebras; Quantum symmetries; Invariant connections (search for similar items in EconPapers)
Date: 2016
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-26902-3_11

Ordering information: This item can be ordered from
http://www.springer.com/9783319269023

DOI: 10.1007/978-3-319-26902-3_11

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().