Quantum gravity, dynamical phase-space and string theory

In a natural extension of the relativity principle, we speculate that a quantum theory of gravity involves two fundamental scales associated with both dynamical spacetime as well as dynamical momentum space. This view of quantum gravity is explicitly realized in a new formulation of string theory which involves dynamical phase-space and in which spacetime is a derived concept. This formulation naturally unifies symplectic geometry of Hamiltonian dynamics, complex geometry of quantum theory and real geometry of general relativity. As a result, the spacetime and momentum space dynamics, and thus dynamical phase-space, is governed by a new version of the renormalization group (RG).