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In loop quantum cosmology the quantum dynamics is well understood.
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T. Schilling, PhD Thesis, Pennsylvania State University 1996; A. Ashtekar and T. Schilling, arXiv:gr-qc/9706069
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A Ashtekar, J. Lewandowski, Class. Quant. Grav. 18 (2001) L117-L128
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A. Ashtekar, M. Bojowald, J. Lewandowski, Adv. Theor. Math. Phys., 7,233, 2003
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A. Ashtekar, S. Fairhurst, J. Willis, Class. Quant. Grav. 20 (2003) 1031;
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A. Ashtekar and J. Lewandowski, Class. Quant. Grav. 21, R53-R152 (2004)
2004
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C. Rovelli, Quantum Gravity
2004
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J. Willis, PhD Thesis, Pennsylvania State University 2004
2004
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M. Bojowald, Living Rev. Relativity 8, (2005), 11
2005
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A. Ashtekar, T. Pawlowski, P. Singh, Phys.Rev.Lett. 96 (2006) 141301; Phys.Rev. D73 (2006) 124038; Phys.Rev. D74 (2006) 084003
2006
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T. Thiemann, Introduction to Modern Canonical Quantum General Relativity
2007
Later among the works it cites.
A. Ashtekar, Nuovo Comento B 122 (2007) 135
2007
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M. Bojowald, Rev.Math.Phys. 18 (2006) 713-746; M. Bojowald, Phys. Rev. Lett. 100 (2008) 221301
2008
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J. Mielczarek, M. Szydlowski, Phys. Rev. D77 (2008) 124008; O. Hrycyna, J. Mielczarek, M. Szydlowski, arXiv:gr-qc/0804.2778v2
2008
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J. Mielczarek, T. Stachowiak, M. Szydlowski, Phys. Rev.D 77, 123506 (2008); M. Szydlowski, W. Godlowslki, T. Stachowiak, Phys. Rev. D 77, 043530 (2008)
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