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CCCC – p. 2 Background independence Background independent quantizations of gravity must show that some form of space-time “emerges” at sufficiently low curvature. Not guaranteed. Canonical approaches: constraints are quantized, receive quantum corrections. Not just dynamics but also space-time structure (gauge content) may change. S = 1 16πG ∫ d 4 x √ |detg| ( ) R+αR 2 +βR ab R ab +··· ? Must know space-time structure before deciding which covariant combinations of metric derivatives can appear. Not just R may receive quantum corrections but also “d 4 x,” or nature of covariance and space-time tensors.
CCCC – p. 3 Loop quantum gravity −→ Holonomies h e = exp( ∫ e dλAi aė a τ i ) along curves e in space. Represented as operators, but not continuous in connection. No connection operator. −→ Holonomies as ladder operators raise excitation level of geometry by discrete steps. Densitized triad quantized as flux ∫ S d2 yn a Ê a i for surfaces S in space, with discrete spectrum containing zero. −→ Spatially diffeomorphism invariant: sum over all deformed graphs. Background independent: No metric used in basic operators. More tricky: Space-time covariance, Hamiltonian constraint. Background independence often forsaken at this stage.
Page 1: CCCC - p. 1 Covariant Canonical Cwa
Page 5 and 6: CCCC - p. 5 Hypersurface-deformatio
Page 7 and 8: CCCC - p. 7 Energy conservation [wi
Page 9 and 10: CCCC - p. 9 Effective canonical dyn
Page 11 and 12: CCCC - p. 11 Low energy effective a
Page 13 and 14: CCCC - p. 13 Effective constraints
Page 15 and 16: CCCC - p. 15 Relevance of effective
Page 17 and 18: CCCC - p. 17 Deformed deformations
Page 19 and 20: CCCC - p. 19 Cosmological perturbat
Page 21 and 22: CCCC - p. 21 Holonomy corrections H
Page 23 and 24: CCCC - p. 23 Ill-posed bounce Bounc
Page 25: CCCC - p. 25 Models of quantum spac

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