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..."but we do not have quantum gravity." This phrase is often used when analysis of a physical problem enters the regime in which quantum gravity effects should be taken into account.
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A. Ashtekar, M. Bojowald, J. Lewandowski (2003) “Mathematical structure of loop quantum cosmology” Adv. Theor. Math. Phys
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C. Rovelli (2004) “Quantum Gravity” (Cambridge University Press, Cambridge)
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A. Ashtekar, J. Lewandowski (2004) “Background independent quantum gravity: a status report.” Class. Quantum Grav
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M. Domagała, J. Lewandowski (2004) “Black-hole entropy from quantum geometry” Class. Quantum Grav
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K. Giesel and T. Thiemann. Algebraic quantum gravity (AQG) I. Conceptual setup. Class. Quant. Grav. 24 (2007) 2465-2498. [gr-qc/0607099]
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W. Kamiński, J. Lewandowski, T. Pawłowski (2009) “Quantum constraints, Dirac observables and evolution: group avereging versus Schrodinger picture in LQC” Class. Quantum Grav
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W. Kamiński, J. Lewandowski, T. Pawłowski (2009) “Physical time and other conceptual issues of quantum gravity on the example of loop quantum cosmology” Class. Quantum Grav
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W. Kaminski, T. Pawlowski (2010) “The LQC evolution operator of FRW universe with positive cosmological constant” Phys. Rev
2010
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K. Giesel, T. Thiemann (2010) “Algebraic quantum gravity (AQG). IV. Reduced phase space quantisation of loop quantum gravity.” Class. Quantum Grav
2010
Closest in time.