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I. M. Khalatnikov and E. M. Lifshitz: Phys. Rev. Lett., 24:76–79, (1970), V. A. Belinsky, I. M. Khalatnikov, and E. M. Lifshitz: Adv. Phys., 19:525–573, (1970), Adv. Phys., 31:639–667, (1982)
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E. Anderson, J. Barbour, B. Z. Foster, B. Kelleher and N. O. Murchadha: Class. Quant. Grav. 22, 1795 (2005) [arXiv:gr-qc/0407104], J. Barbour and N. O. Murchadha: arXiv:1009.3559
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Then

J. Barbour: arXiv:1105.0183, H. Gomes, S. Gryb and T. Koslowski: Class. Quant. Grav. 28
Original
2011
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2011

Shape Dynamics

Koslowski, Tim

Understand

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.