Canonical quantum gravity and effective theory

Effective actions provide a powerful way to understand low-energy, semiclassical or other regimes of quantum field theories. Although canonical quantum gravity theories, such as loop quantum gravity, are not directly accessible to the usual techniques of computing effective actions, equivalent methods to derive an effective Hamiltonian and effective equations have recently been developed. This provides means to study the semiclassical limit of loop quantum gravity, demonstrating the correct approach to classical behavior and including quantum correction terms. Salient features of loop quantum gravity, its effective equations and applications in cosmological regimes are discussed.