Karim Thebault (MCMP/LMU) gives a talk at the Irvine-Munich Workshop on the Foundations of Classical and Quantum Field Theories (14 December, 2014) titled "A New Prescription for the Quantization of Refoliation Invariant Field Theories". Abstract: Imagine a loaf of bread that we can irregularly cut up into a sequence of slices. The loaf is spacetime and the slices are instantaneous spatial surfaces. A foliation is a parameterization of a spacetime by a time ordered sequence of spatial slices. In a field theory such a parametrization can be local in the sense that it is defined for every point on every spatial slice. Diffeomorphism invariance implies that spacetimes described by general relativity that are related by refoliations are physically equivalent. Classically the symmetry is therefore directly connectable to the idea that only the coordinate-free information contained in a spacetime geometry has a physical basis. The implications of this symmetry for quantization are notoriously problematic. Here we offer a new prescription for the canonical quantization of gravity that side-steps the issues with refoliations via the adoption of the 'shape dynamics’ reformulation. We then offer our thoughts as to whether this is a satisfactory resolution for the problem for understanding refoliation symmetry in the context of a quantum field theory of gravity.