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CCCC – p. 14 Effective constraint algebras Systems with several classical constraints C I : → Effective constraints C I,pol = 〈̂polĈI〉(〈·〉,∆(·)) with ̂pol polynomial in basic operators. → Compute effective constraint algebra by Poisson brackets. Easier than commutators of operators. Parameterizable. → Check off-shell consistency of first-class constraints. Example: Hamiltonian and diffeomorphism constraints obey hypersurface-deformation algebra of classical space-time. {D[w a 1],D[w a 2]} = −D[L w2 w a 1] {H[N],D[w a ]} = −H[w a ∇ a N] {H[N 1 ],H[N 2 ]} = D[h ab (N 1 ∇ b N 2 −N 2 ∇ b N 1 )]
CCCC – p. 15 Relevance of effective methods → “Big-bang state” largely unknown. Consider generic states in effective parameterization. → Local internal times: Do not require artificial matter contents such as free, massless scalar or dust. → No gauge-fixing or deparameterization, or solution of classical constraints required before quantization: Check off-shell consistency of constraint algebra and corresponding space-time structure. Quantum space-time structure derived, not presupposed. Surprises . . .
Page 1 and 2: CCCC - p. 1 Covariant Canonical Cwa
Page 3 and 4: CCCC - p. 3 Loop quantum gravity
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: CCCC - p. 13 Effective constraints
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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