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Canonical quantum gravity provides insights into the quantum dynamics as wellas quantum geometry of space-time by its implications for constraints. Loopquantum gravity in particular requires specific corrections due to itsquantization procedure, which also results in a discrete picture of space. Thecorresponding changes compared to the classical behavior can most easily beanalyzed in isotropic models, but perturbations around them are more involved.For one type of corrections, consistent equations have been found which shedlight on the underlying space-time structure at the Planck scale: not justquantum dynamics but also the concept of space-time manifolds changes inquantum gravity. Effective line elements provide indications for possiblerelationships to other frameworks, such as non-commutative geometry.

Quantum geometry and quantum dynamics at the Planck scale