Mathematical structure of loop quantum cosmology

@article{Ashtekar2003MathematicalSO,
  title={Mathematical structure of loop quantum cosmology},
  author={Abhay Ashtekar and Martin Bojowald and Jerzy Lewandowski},
  journal={Advances in Theoretical and Mathematical Physics},
  year={2003},
  volume={7},
  pages={233-268}
}
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… 
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