Abstract
As an important alternative quantum theory of general relativity, loop quantum gravity has made considerable progress. At present, a key and difficult issue in loop quantum gravity is to build a reasonable quantum dynamics. In the canonical formulation of loop quantum gravity, it requires us to construct a reasonable Hamiltonian constraint operator and then solve the quantum constraint equation. In this paper, we will review the basic ideas of loop quantum gravity and its quantum dynamics. We will mainly focus on the construction of Hamiltonian constraint operators and the corresponding Hilbert spaces in which the Hamiltonian constraint operators can be well defined.
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