Hamiltonian Theory: Dynamics

Abstract

This chapter focuses on the status of the implementation of the dynamics in the canonical version of Loop Quantum Gravity (LQG). Concretely this means to provide a mathematical meaning of the quantum Einstein equations, sometimes called Wheeler-DeWitt equations, to give a physical interpretation and Hilbert space structure to its solutions and to construct a representation of the algebra of observables including a physical Hamiltonian. This is a structural overview intentionally skipping technical details.

52 pages. This is a preprint of a chapter to appear in the "Handbook of Quantum Gravity", edited by Cosimo Bambi, Leonardo Modesto and Ilya Shapiro, 2023, Springer, reproduced with permission of Springer