Introduction to Shape Dynamics

Seminar Talk in Frederic Schuller’s group, Max Planck Institute for Gravitational Physics

In the first part of my talk, I want to explain how constraints can arise after performing the Legrendre transform to restrict the physical phase space to a submanifold. This enables me to explain certain aspects of the Dirac procedure and how we can classify constraints. Finally, I hope to give new insights for the understanding of gauge degrees of freedom in the Hamiltonian picture.
In the main part of my talk, I will carefully explain how Shape Dynamics can be defined from General Relativity using a Linking Theory in the Hamiltonian formulation. It can be shown that Shape Dynamics is a theory of gravity which has the Dirac observables and encodes the same dynamics as General Relativity, but has conformal gauge orbits instead of local time reparametrization.