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CCCC – p. 6 Background independence? Status of background independence in loop quantum gravity: (+) No spatial background metric used to define states and operators, summed over spatial diffeomorphisms. Uniqueness of representation. (−) Hamiltonian constraint quantized in much more messy way. Modify classical expression by holonomy corrections (quantum corrections mixed with regulator). (−) Diffeomorphism constraint and Hamiltonian constraint contain curvature of A i a, but treated differently. (−) Off-shell algebra of Hamiltonian constraints often ignored. [see also H Nicolai, K Peeters, M Zamaklar: hep-th/0501114] Can this procedure result in any consistent space-time picture? Energy conservation?
CCCC – p. 7 Energy conservation [with M Kagan, G Hossain, C Tomlin: arXiv:1302.5695] N √ deth∇ µ T µ 0 = −N ∂H matter ∂t −N a∂Dmatter a ∂t +L ⃗N C matter [N,N a ]+ ∂h ab ∂t +∂ b ( N 2 h ab D matter a δH matter δh ab ) +2N c h baδH matter δh ac Classical off-shell algebra: ∂H matter /∂t = {H matter ,H[N,N a ]} cancels ∂ a (N 2 D matter a ), only one term from ∂ b T b 0. → Deformed algebra cannot be taken care of by modified coefficients in ∇ µ T µ ν = 0. → No energy conservation if off-shell algebra broken (or unchecked in gauge-fixed/deparameterized models).
Page 1 and 2: CCCC - p. 1 Covariant Canonical Cwa
Page 3 and 4: CCCC - p. 3 Loop quantum gravity
Page 5: CCCC - p. 5 Hypersurface-deformatio
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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