470 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)233-268
Number of pages36
JournalAdvances in Theoretical and Mathematical Physics
Volume7
Issue number2
DOIs
StatePublished - Jan 1 2003

Fingerprint

Quantum Cosmology
cosmology
Reduced Model
geometry
Cosmology
Quantization
Singularity
Symmetry
symmetry

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Physics and Astronomy(all)

Cite this

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abstract = "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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Mathematical structure of loop quantum cosmology. / Ashtekar, Abhay; Bojowald, Martin; Lewandowski, Jerzy.

In: Advances in Theoretical and Mathematical Physics, Vol. 7, No. 2, 01.01.2003, p. 233-268.

Research output: Contribution to journalArticle

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