Shape Dynamics: General Relativity reloaded

AIMS Journal Club Talk, African Institute for Mathematical Sciences in Sénégal

Shape Dynamics (SD) is a reformulation of Einstein’s General Relativity (GR), the well-tested classical description of gravity. Based on the ADM formulation of General Relativity one can construct Shape Dynamics through symmetry trading: the local time reparametrization invariance (Hamiltonian constraint) is replaced by a local conformal symmetry of the 3-metric (conformal constraint). Shape Dynamics and General Relativity are therefore linked by their Hamiltonian formulation: both live in the ADM phase space, but on different constraint surfaces. Where the two surfaces intersect, the Hamiltonian flows coincide, leading to equivalent dynamics and an explicit dictionary between observables of the two theories. However, the conformal constraint is linear in the momenta which makes Shape Dynamics much more suitable for a naïve quantization. Furthermore, Shape Dynamics provides useful tools for cosmological calculations as it allows an easy treatment of the gauge symmetry because its Dirac observables are manifest. In my talk, I will review the construction of shape dynamics and my current research on new calculation techniques for cosmological models.