Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-07-11
Mod.Phys.Lett.A25:2381,2010
Physics
High Energy Physics
High Energy Physics - Theory
Invited Review for Mod. Phys. Lett. A, 17 pages
Scientific paper
10.1142/S0217732310034067
We explain how quantum gravity can be defined by quantizing spacetime itself. A pinpoint is that the gravitational constant G = L_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 L_P. The symplectic structure of spacetime M leads to an isomorphism between symplectic geometry (M, \omega) and Riemannian geometry (M, g) where the deformations of symplectic structure \omega in terms of electromagnetic fields F=dA are transformed into those of Riemannian metric g. This approach for quantum gravity allows a background independent formulation where spacetime as well as matter fields is equally emergent from a universal vacuum of quantum gravity which is thus dubbed as the quantum equivalence principle.
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