Advances in Theoretical and Mathematical Physics

Volume 7 (2003)

Number 2

Mathematical structure of loop quantum cosmology

Pages: 233 – 268



Abhay Ashtekar

Martin Bojowald

Jerzy Lewandowski


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.

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