Abstract
The gravity is classically formulated as the geometric curvature of the space-time in general relativity which is completely different from the other well-known physical forces. Since seeking a quantum framework for the gravity is a great challenge in physics. Here we present an alternative construction of quantum gravity in which the quantum gravitational degrees of freedom are described by the non-Abelian gauge fields characterizing topological non-triviality of the space-time. The quantum dynamics of the space-time thus corresponds to the superposition of the distinct topological states. Its unitary time evolution is described by the path integral approach. This result will also be suggested to solve some major problems in physics of the black holes.
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