  General Relativity can be reformulated as a geometrodynamical theory, called
Shape Dynamics, that is not based on spacetime (in particular refoliation)
symmetry but on spatial diffeomorphism and local spatial conformal symmetry.
This leads to a constraint algebra that is (unlike General Relativity) a Lie
algebra, where all local constraints are linear in momenta and may thus be
quantized as vector fields on the geometrodynamic configuration space. The
Hamiltonian of Shape Dynamics is complicated but admits simple expressions
whenever spatial derivatives are negligible.
