Shape Dynamics

TL;DR

Shape Dynamics offers an alternative formulation of General Relativity emphasizing spatial conformal symmetry, resulting in a Lie algebra structure that simplifies quantization and provides new insights into gravitational dynamics.

Contribution

It introduces a reformulation of General Relativity called Shape Dynamics, replacing spacetime refoliation invariance with spatial conformal symmetry, leading to a Lie algebra of constraints.

Findings

Constraint algebra forms a Lie algebra, unlike in GR.

All local constraints are linear in momenta, facilitating quantization.

Simplified expressions for the Hamiltonian when spatial derivatives are negligible.

Abstract

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.