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CCCC – p. 8 Consistent loop quantum gravity → Off-shell closed operator algebra of constraints likely? → Semiclassical states (at dynamical level)? More realistic (at least in particle-physics analogy): Effective equations. → Ease subtleties of factor ordering and quantum representation. → Describe general classes of semiclassical states without requiring full wave function. (Vacuum problem of quantum gravity.) → Can be generalized to constrained systems. Allow local internal times and time changes by gauge transformations. → Simpler derivation of closed constraint algebras. But still incomplete.
CCCC – p. 9 Effective canonical dynamics Parameterize state by expectation values 〈ˆq〉 and 〈ˆp〉 of basic operators and moments (Includes mixed states.) G a,n = 〈(ˆq −〈ˆq〉) a (ˆp−〈ˆp〉) n−a 〉 symm Commutator of operators determines Poisson bracket of moments. (Symplectic space, but not after restriction to finite n.) Expectation value of Hamiltonian, interpreted as function of 〈ˆq〉, 〈ˆp〉 and G a,n , provides canonical equations of motion. Effective equations: Correct classical equations for 〈ˆq〉, 〈ˆp〉 by quantum back-reaction from moments. [with A Skirzewski: math-ph/0511043]
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: CCCC - p. 7 Energy conservation [wi
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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