2003/04/30 by Abhay Ashtekar, Martin Bojowald, Jerzy Lewandowski · 2 citations
Physics and Astronomy · Mathematics · #gr-qc #hep-th #math-ph #math.MP
published as Adv.Theor.Math.Phys.7:233-268,2003 · 29 pages, v2: minor corrections, v3: remark added in appendix
arxiv created 2003/12/24 · arxiv updated 2011/05/05
Applications of Riemannian quantum geometry to cosmology have had notable successes. In particular, the fundamental discreteness underlying quantum geometry has led to a natural resolution of the big bang singularity. However, the precise mathematical structure underlying loop quantum cosmology and the sense in which it implements the full quantization program in a symmetry reduced model has not been made explicit. The purpose of this paper is to address these issues, thereby providing a firmer mathematical and conceptual foundation to the subject.