Emergent Geometry and Quantum Gravity

  title={Emergent Geometry and Quantum Gravity},
  author={Hyun S. Yang},
We explain how quantum gravity can be defined by quantizing spacetime itself. A pinpoint is that the gravitational constant $G = L_{\rm P}^2$ whose physical dimension is of (length)2 in natural unit introduces a symplectic structure of spacetime which causes a noncommutative spacetime at the Planck scale LP. The symplectic structure of spacetime M leads to an isomorphism between symplectic geometry (M, ω) and Riemannian geometry (M, g) where the deformations of symplectic structure ω in terms… CONTINUE READING